Generated by All in One SEO v5.0.1.1, this is an llms.txt file, used by LLMs to index the site. # Civil Thinking Civil Engineering Simulations and live classes ## Sitemaps - [XML Sitemap](https://civilthinking.com/sitemap.xml): Contains all public & indexable URLs for this website. ## Posts - [Loaded Beam under Distributed Loading](https://civilthinking.com/beam-analysis-problems/beam-subjected-to-distributed-loading-a-prismatic-beam-of-span-3-m-is-subjected-to-the-following-loading-and-support-conditions-supports-support-at-x-0-m-support-at-x-3-m/) - Beam Subjected to Distributed Loading A prismatic beam of span 3 m is subjected to the following loading and support conditions. Supports: • Support at x… - [Zulfy Rajab](https://civilthinking.com/employees-at-civil-thinking/zulfy-rajab/) - Roles: Founder and Engineer at Civil Thinking (https://civilthinking.com) - [SOLUTION OF PROBLEM 2/6 Two forces are applied to the construction bracket as shown. Determine the angle θ which makes the resultant of the two forces vertical. Determine the magnitude R of the resultant.](https://civilthinking.com/qna/statics/force-system/solution-of-problem-2-6-two-forces-are-applied-to-the-construction-bracket-as-shown-determine-the-angle-θ-which-makes-the-resultant-of-the-two-forces-vertical-determine-the-magnitude-r-of-the-r/) - Solution: Below is the solution of this statics force system problem. You may download the solution PDF file: SOLUTION OF 2 6 Two forces are applied to the construction bracket as shown Determine the angle θ which makes the resultant of the two forces verticalDownload the Solution - [SOLUTION OF PROBLEM 2/4 The line of action of the 3000-lb force runs through the  points A and B as shown in the figure. Determine the x and  y scalar components of F](https://civilthinking.com/qna/statics/force-system/solution-of-problem-2-4-the-line-of-action-of-the-3000-lb-force-runs-through-the-points-a-and-b-as-shown-in-the-figure-determine-the-x-and-y-scalar-components-of-f/) - Solution: Below is the solution of this Statics Problem. You may download the solution file: SOLUTION OF 2 4 The line of action of the 3000-lb force runs through the points A and B as shown in the figure. Determine the x and y scalar components of FDownload the Solution - [SOLUTION OF PROBLEM 2/3 The slope of the 6.5-kN force F is specified as shown in the figure. Express F as a vector in terms of the unit vectors i and j.](https://civilthinking.com/qna/statics/force-system/solution-of-problem-2-3-the-slope-of-the-6-5-kn-force-f-is-specified-as-shown-in-the-figure-express-f-as-a-vector-in-terms-of-the-unit-vectors-i-and-j/) - Solution: Below is the Solution of this Statics problem. You may download the Solution PDF: SOLUTION OF 2 3 The slope of the 6.5-kN force F is specified as shown in the figure. Express F as a vector in terms of the unit vectors i and jDownload the Solution - [SOLUTION OF PROBLEM: 1/2 Determine the magnitude of the vector sum V= V1 + V2 and the angle θx which V makes with the positive x-axis. Complete both graphical and algebraic solutions.](https://civilthinking.com/qna/statics/force-system/solution-of-problem-1-2-determine-the-magnitude-of-the-vector-sum-v-v1-v2-and-the-angle-θx-which-v-makes-with-the-positive-x-axis-complete-both-graphical-and-algebraic-solutions/) - Solution: Below is the solution of this Force Resultant problem, using both graphic and algebraic methods. You may download the solution file: SOLUTION OF Determine the magnitude of the vector sum V= V1 + V2 and the angle θx which V makes with the positive x-axis. Complete both graphical and algebraic solutionsDownload the Solution - [SOLUTION OF: Determine the force in members GE, GC, and BC o the truss shown in Fig. 6-16a. Indicate whether the members are in tension or compression.](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-using-method-of-sections-problem-solution/solution-of-determine-the-force-in-members-ge-gc-and-bc-o-the-truss-shown-in-fig-6-16a-indicate-whether-the-members-are-in-tension-or-compression/) - Solution: Below is the solution of this truss analysis problem using method of sections: - [SOLUTION OF: A pin-jointed truss supported by a pinned support at A and a roller support at G carries three loads at joints C, D and E as shown in the Figure. Determine the magnitude and sense (i.e. tension / compression) of the forces induced in members DE, IE AND IH as indicated?](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-using-method-of-sections-problem-solution/solution-of-a-pin-jointed-truss-supported-by-a-pinned-support-at-a-and-a-roller-support-at-g-carries-three-loads-at-joints-c-d-and-e-as-shown-in-the-figure-determine-the-magnitude-and-sense-i-e-t/) - Solution: Below is the solution of this Truss Analysis problem using Method of Sections: - [SOLUTION OF: Determine the force in each member of the truss shown in Fig. 6-10a and indicate whether the members are in tension or compression.](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-by-method-of-joints/solution-of-determine-the-force-in-each-member-of-the-truss-shown-in-fig-6-10a-and-indicate-whether-the-members-are-in-tension-or-compression/) - Solution: Below is the solution of this truss analysis problem using Method of Joints: - [SOLUTION OF: Determine the force in each member of the truss shown in Fig. 6-8a and indicate whether the members are in tension or compression](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-by-method-of-joints/solution-of-determine-the-force-in-each-member-of-the-truss-shown-in-fig-6-8a-and-indicate-whether-the-members-are-in-tension-or-compression/) - Solution: Below is the solution of this Truss Analysis problem using method of Joints: - [SOLUTON OF: Determine the horizontal and vertical components of reactions on the beam caused by the pin at B and the rocker at A as shown in Fig. 5-12a. Neglect the weight of the beam.](https://civilthinking.com/qna/statics/beam-analysis-statics/support-reactions-in-beams/soluton-of-determine-the-horizontal-and-vertical-components-of-reactions-on-the-beam-caused-by-the-pin-at-b-and-the-rocker-at-a-as-shown-in-fig-5-12a-neglect-the-weight-of-the-beam/) - Solution: Below is the solution of this support reaction problem of simply supported bam carrying an inclined load: - [Determine the reactions on the beam shown in the figure below. The beam is a 5m long cantilever, with fixed support at left side. The beam carries two point loads of 10kN and 20kN at a distance of 2m and 5m from left support respectively. The beam also carries an axial load of 15kN, towards right, at the free end.](https://civilthinking.com/qna/statics/beam-analysis-statics/support-reactions-in-beams/determine-the-reactions-on-the-beam-shown-in-the-figure-below-the-beam-is-a-5m-long-cantilever-with-fixed-support-at-left-side-the-beam-carries-two-point-loads-of-10kn-and-20kn-at-a-distance-of-2m/) - Solution: Below is the solution of this cantilever beam with axial load problem: - [SOLUTION OF: Determine the reactions on the beam shown in the figure below. The simply supported beam carries a point load at 2m from left pin support. The total length of the beam is 8m and it also carries an axial load of 50kN towards right.](https://civilthinking.com/qna/statics/beam-analysis-statics/support-reactions-in-beams/solution-of-determine-the-reactions-on-the-beam-shown-in-the-figure-below-the-simply-supported-beam-carries-a-point-load-at-2m-from-left-pin-support-the-total-length-of-the-beam-is-8m-and-it-also-c/) - Solution: Below is the solution of this support reactions in simply supported beam carrying an axial load problem: - [SOLUTION OF: Determine the reactions on the beam shown in the figure below. The beam is a simply supported beam with 20kN load at mid point. Total length of beam is 4m.](https://civilthinking.com/qna/statics/beam-analysis-statics/support-reactions-in-beams/solution-of-determine-the-reactions-on-the-beam-shown-in-the-figure-below-the-beam-is-a-simply-supported-beam-with-20kn-load-at-mid-point-total-length-of-beam-is-4m/) - Below is the solution of finding support reaction in simply supported beam with point load at middle: - [Determine the stretch in each spring for equilibrium of the 2-kg block. The springs are shown in the equilibrium position.](https://civilthinking.com/qna/statics/analysis-of-cords-and-springs-in-statics-using-equilibrium-equations/determine-the-stretch-in-each-spring-for-equilibrium-of-the-2-kg-block-the-springs-are-shown-in-the-equilibrium-position/) - Solution: Below is the solution file of this spring analysis problem in Statics and Mechanics. You may download the solution file. SOLUTION OF Determine the stretch in each spring for equilibrium of the 2-kg block. The springs are shown in the equilibrium positionDownload the solution - [SOLUTION OF: Determine the required length of cord AC in fig. 3-8a so that the  8-kg lamp can be suspended in the position shown. The unstretched length of spring AB is l'AR = 0.4 m, and the spring has a stiffness of kAB = 300 N/m.](https://civilthinking.com/qna/statics/analysis-of-cords-and-springs-in-statics-using-equilibrium-equations/solution-of-determine-the-required-length-of-cord-ac-in-fig-3-8a-so-that-the-8-kg-lamp-can-be-suspended-in-the-position-shown-the-unstretched-length-of-spring-ab-is-lar-0-4-m-and-the-spr/) - Solution: Below is the solution file of this Cord and cable analysis problem in Statics. You may download the solution: Determine the required length of cord AC in fig. 3-8a so that the 8-kg lamp can be suspended in the position shown. The unstretched length of spring AB is l'ARDownload the Solution - [SOLUTION OF Problem: Three cables are joined at the junction right C. Determine the tensions in cables AC and BC caused by the weight of 30-kg cylinder.](https://civilthinking.com/qna/statics/cable-analysis-problem-solutions/solution-of-problem-three-cables-are-joined-at-the-junction-right-c-determine-the-tensions-in-cables-ac-and-bc-caused-by-the-weight-of-30-kg-cylinder/) - Solution: Below is the Solution of this cable analysis problem in Statics and Mechanics. - [SOLUTION OF: Find the load-bearing capacity as per Eurocode of a column loaded axially with the cross-section, as a complex section made of two C300 sections and two cover plates as shown below. The column is 6,00m high with pivots at the ends. Steel grade S355, strength fyd=355Mpa, E= 210Gpa.](https://civilthinking.com/qna/statics/statics-eurocode-problem-solutions/solution-of-find-the-load-bearing-capacity-as-per-eurocode-of-a-column-loaded-axially-with-the-cross-section-as-a-complex-section-made-of-two-c300-sections-and-two-cover-plates-as-shown-below-the-c/) - Solution: Below is the solution in PDF format of this Eurocode-3 Buckling Problem. You may download the Solution file: Problem Solution of finding the load bearing capacity of a Column as per Eurocode-3 cross-section C300Download the Solution - [Parallel Axis Theorem in Moment of Inertia](https://civilthinking.com/tutorials/statics-and-mechanics-lessons-tutorials/center-of-gravity-and-moment-of-inertia-concepts/parallel-axis-theorem-in-moment-of-inertia/) - Moment of inertia about an axis that pass through other than axis through center of gravity = moment of inertia about axis passing through center of gravity + (Area of Shape* (distance between the axis about which we are finding the moment of inertia and axis passing through center of gravity)^2) No need to remember - [Moment of Inertia Table of basic shapes: Rectangle, Triangle, and Circle: jpeg image](https://civilthinking.com/tutorials/statics-and-mechanics-lessons-tutorials/center-of-gravity-and-moment-of-inertia-concepts/moment-of-inertia-table-of-basic-shapes-rectangle-triangle-and-circle-jpeg-image/) - [Moment of Inertia Table of Basic Shapes: Rectangle, Triangle, and Circle](https://civilthinking.com/tutorials/statics-and-mechanics-lessons-tutorials/center-of-gravity-and-moment-of-inertia-concepts/moment-of-inertia-table-of-basic-shapes-rectangle-triangle-and-circle/) - CENTROID AND MOMENT OF INERTIA OF Basic PLANE AREAS Table Area, centroid coordinates, Ix and IYDownload the Inertia Table - [Find the moment of Inertia Ix and Iy of the shown C section. x and y are the axes passing through center of gravity of the C section](https://civilthinking.com/qna/statics/center-of-gravity-and-moment-of-inertia-problem-solutions/find-the-moment-of-inertia-ix-and-iy-of-the-shown-c-section-x-and-y-are-the-axes-passing-through-center-of-gravity-of-the-c-section/) - Solution: Below is the Solution of this Center of gravity and Moment of Inertia problem. You may download the solution: SOLUTION OF Find the moment of Inertia Ix and Iy of the c section shownDownload the solution - [Statics and Mechanics Solved Problems for Learning](https://civilthinking.com/uncategorized/statics-and-mechanics-solved-problems-for-learning/) - We have solve numerous problems on Statics and Mechanics, covering topics from force systems, shear and moment diagrams, shear stresses, bending stresses, compression and tension members, principal stresses, and more. Below are the links to access these solved problems: Beam Analysis Support Reactions in Beams Center of Gravity and Moment of Inertia of different Cross - [Please find the coordinates of center of gravity x₀, y₀, of the composite section made of C180 and I200 Eurocode sections](https://civilthinking.com/qna/statics/center-of-gravity-and-moment-of-inertia-problem-solutions/center-of-gravity-and-moment-of-inertia-of-eurocode-based-cross-section-problem-solutions/please-find-the-coordinates-of-center-of-gravity-x₀-y₀-of-the-composite-section-made-of-c180-and-i200-eurocode-sections/) - Solution: Below is the Solution of this center of gravity problem. You may download the solution: SOLUTION OF Please find the coordinates of center of gravity x0, y0, of the composite section made of C180 and I200 eurocode sectionsDownload the Solution - [Trick on: How to identify zero force members in Trusses without Analysis](https://civilthinking.com/tutorials/statics-and-mechanics-lessons-tutorials/trick-on-how-to-identify-zero-force-members-in-trusses-without-analysis/) - Trick to identify the zero force members in a truss without analysisDownload the Lesson - [Please find the axial force in the following truss members, cut by the section α-α, using Ritter's method.](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-using-ritters-method/please-find-the-axial-force-in-the-following-truss-members-cut-by-the-section-α-α-using-ritters-method/) - Solution: Below is the solution of this Truss Analysis problem. You may download the solution file. SOLUTION OF Please find the forces in the members of the truss, shown using alpha alpha cut line using ritter's method prob3Download the Solution - [Please find the forces in members of the following truss in α-α section using Ritter's Method](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-using-ritters-method/please-find-the-forces-in-members-of-the-following-truss-in-α-α-section-using-ritters-method/) - Solution: Below is the solution of this Truss Analysis problem, using Ritter's method. You may download the Solution: SOLUTION OF Please find the forces in the members of the truss, shown using alpha alpha cut line using ritter's method prob2Download the Solution - [Please find the forces in members in α-α section using Ritter method](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-using-ritters-method/please-find-the-forces-in-members-in-α-α-section-using-ritter-method/) - Solution: Below is the solution of this Truss problem. You may download the solution: SOLUTION OF Please find the forces in the members of the truss, shown using alpha alpha cut line using ritter's methodDownload the Solution - [Simply Supported Beam with Point Load](https://civilthinking.com/beam-analysis-problems/simply-supported-beam-with-point-load-a-prismatic-beam-of-span-1-m-is-subjected-to-the-following-loading-and-support-conditions-supports-support-at-x-0-m-support-at-x-1-m/) - Simply Supported Beam with Point Load A prismatic beam of span 1 m is subjected to the following loading and support conditions. Supports: • Support at x… - [Loaded Beam under Distributed Loading](https://civilthinking.com/beam-analysis-problems/beam-subjected-to-distributed-loading-a-prismatic-beam-of-span-1-m-is-subjected-to-the-following-loading-and-support-conditions-supports-support-at-x-0-m-support-at-x-1-m/) - Beam Subjected to Distributed Loading A prismatic beam of span 1 m is subjected to the following loading and support conditions. Supports: • Support at x… - [Reinforced Concrete Structures online Tutor Available!](https://civilthinking.com/uncategorized/reinforced-concrete-structures-online-tutor-available/) - If you need Online tutoring in RCC/ Reinforced Concrete Structures contact us. Know More - [Structural Analysis Online Tutor Available](https://civilthinking.com/uncategorized/structural-analysis-online-tutor-available/) - If you need an online tutor to learn Structural Analysis, we can help. We teach Structural Analysis complete course online. Know More - [Mechanics of Materials Online Tutor](https://civilthinking.com/uncategorized/mechanics-of-materials-online-tutor/) - If you need a tutor to learn Mechanics of Materials/ Strength of Materials, contact us. We offer online tutoring in Mechanics of Materials / Strength of Materials Know More - [Statics Online Tutorials](https://civilthinking.com/uncategorized/statics-online-tutorials/) - We offer online tutorials in Statics/ Mechanics. Know More - [Please find forces RA and RB balancing the force system P1=100kN and P2=30kN. Forces RA and RB are on lines a and b parallel to lines of action of forces P1 and P2. Use graphic and numerical methods](https://civilthinking.com/qna/statics/force-system/please-find-forces-ra-and-rb-balancing-the-force-system-p1100kn-and-p230kn-forces-ra-and-rb-are-on-lines-a-and-b-parallel-to-lines-of-action-of-forces-p1-and-p2-use-graphic-and-numerical-methods/) - Solution: Below is the solution of this Parallel Force System Equilibrium Problem, solved using both numeric and graphic method. You may download the solution. Please find forces RA and RB balancing the force system P1 100kN and P2 30kN. Forces RA and RB are on lines a and b parallel to lines of action of - [Please find on lines of action a and b two forces parallel to each other and balancing the force P=100kN on line C. Use graphic and numerical methods](https://civilthinking.com/qna/statics/force-system/please-find-on-lines-of-action-a-and-b-two-forces-parallel-to-each-other-and-balancing-the-force-p100kn-on-line-c-use-graphic-and-numerical-methods/) - Solution: Below is the Solution of this Parallel Force System Equilibrium Problem, solved using Graphic Method. You may download the Solution. Please find on lines of action a and b two forces parallel to each other and balancing the force P 100 kN on line C. Use graphic and numerical methodsDownload the Solution - [Please find the force R1 on line of action 1, and force R2 passing through point B in such a way that the forces R1 and R2 balance the system of forces Q1, Q2, Q3 and Q4, using Graphic Method in Statics](https://civilthinking.com/qna/statics/force-system/please-find-the-force-r1-on-line-of-action-1-and-force-r2-passing-through-point-b-in-such-a-way-that-the-forces-r1-and-r2-balance-the-system-of-forces-q1-q2-q3-and-q4-using-graphic-method-in-stati/) - Solution: Below is the Solution of this Parallel Force System Equilibrium Problem, solved using Graphic method. You may download the Solution Please find the force R1 on line of action 1, and force R2 passing through point B in such a way that the forces R1 and R2 balance the system of forces Q1, Q2, - [Please divide the force F=80 kN into two forces located on the straights g and h parallel to the straight of force F.](https://civilthinking.com/qna/statics/force-system/please-divide-the-force-f80-kn-into-two-forces-located-on-the-straights-g-and-h-parallel-to-the-straight-of-force-f/) - Please use the ruler and set-square in the graphic method. Solution: Below is the Solution of this Parallel Force System using Graphic Method. You may download the Solution. Please divide the force F 80 kN into two forces located on the straights g and h parallel to the straight of force FDownload the Solution - [Please divide the force P=1000kN into two forces located on the straights a and b parallel to the straight of force P. Please use the ruler and set-square in the graphic method.](https://civilthinking.com/qna/statics/force-system/please-divide-the-force-p1000kn-into-two-forces-located-on-the-straights-a-and-b-parallel-to-the-straight-of-force-p-please-use-the-ruler-and-set-square-in-the-graphic-method/) - Solution: Below is the Solution of this Parallel Force Resolution problem. You may download the Solution Please divide the force P 1000kN into two forces located on the straights a and b parallel to the straight of force PDownload the Solution - [Please find the resultant force of the coplanar force system using numerical and graphic methods Calculate the moment of forces relative to the origin of coordinate system. Please use the ruler and set-square in the graphic method.](https://civilthinking.com/qna/statics/force-system/please-find-the-resultant-force-of-the-coplanar-force-system-using-numerical-and-graphic-methods-calculate-the-moment-of-forces-relative-to-the-origin-of-coordinate-system-please-use-the-ruler-and-se/) - Solution: Below is the solution of this Coplanar Force System problem. You may download the Solution Please find the resultant force of the coplanar force system using numerical and graphic methods Calculate the moment of forces relative to the origin of coordinate systemDownload the Solution - [Please find the force in bar of the rotary crane loaded by force P=10kN below. Please use the ruler and set-square in the graphic method.](https://civilthinking.com/qna/statics/force-system/please-find-the-force-in-bar-of-the-rotary-crane-loaded-by-force-p10kn-below-please-use-the-ruler-and-set-square-in-the-graphic-method/) - Solution: Below is the solution of this Statics Force problem. You may download the Solution: Please find the force in bar of the rotary crane loaded by force P 10kN below.Download the Solution - [Please find the resultant force caused by the pressure of ground and by dead weight of a concrete retaining wall as shown at the diagram below. H=36kN(pressure of ground), V=52kN(dead weight of wall). Please use the ruler and set-square in the graphic method.](https://civilthinking.com/qna/statics/force-system/please-find-the-resultant-force-caused-by-the-pressure-of-ground-and-by-dead-weight-of-a-concrete-retaining-wall-as-shown-at-the-diagram-below-h36knpressure-of-ground-v52kndead-weight-of-wall/) - Solution: Below is the Solution of this Statics, Force System Problem. You may download the Solution Please find the resultant force caused by the pressure of ground and by dead weight of a concrete retaining wall as shown at the diagram below. H 36 kN (pressure of ground), V 52 kN (dead weight of wall)Download - [Please find the resultant of three forces passing through the origin of coordinates. Forces are perpendicular to one another. P1=12kN, P2=24kN, P3=36kN. Please use the ruler and set-square in the graphic method.](https://civilthinking.com/qna/statics/force-system/please-find-the-resultant-of-three-forces-passing-through-the-origin-of-coordinates-forces-are-perpendicular-to-one-another-p112kn-p224kn-p336kn-please-use-the-ruler-and-set-square-in-the-grap/) - Solution: Below is the solution of this Statics Force System Problem. You may download the solution Please find the resultant of three forces passing through the origin of coordinates. Forces are perpendicular to one another. P1 12kN, P2 24kN, P3 36kNDownload the Solution - [Please find the forces in two parts of the rope suspended between the walls and loaded by the force P= 10kN as on diagram below, using both Analytical Method and Graphical Method in Statics](https://civilthinking.com/qna/statics/force-system/please-find-the-forces-in-two-parts-of-the-rope-suspended-between-the-walls-and-loaded-by-the-force-p-10kn-as-on-diagram-below-using-both-analytical-method-and-graphical-method-in-statics/) - Solution: Below is the Solution of this Problem. You may download the Solution Please find the forces in two parts of the rope suspended between the walls and loaded by the force P 10kN as on diagram belowDownload the Solution - [Closed traverse ABCD has the following bearings AB equals North 45 degrees 20 minutes East BC equals South 47 degrees 32 minutes East CD equals South 14 degrees 55 minutes West and DA equals North 68 degrees 00 minutes West Compute the interior angles and provide a geometric check for your work](https://civilthinking.com/qna/surveying-geomatics-problem-solutions-by-civil-thinking/surveying-geomatics-angles-and-directions-problem-solutions-by-civil-thinking/closed-traverse-abcd-has-the-following-bearings-ab-equals-north-45-degrees-20-minutes-east-bc-equals-south-47-degrees-32-minutes-east-cd-equals-south-14-degrees-55-minutes-west-and-da-equals-north-68/) - Solution: Below is the solution of this Surveying / Geomatics problem. You may download the Solution: Closed traverse ABCD has the following bearings AB equals North 45 degrees 20 minutesDownload the solution - [Prepare a set of profile leveling notes for the survey in Figure. In addition to computing all elevations, show the arithmetic check and the resulting error in closure](https://civilthinking.com/qna/surveying-geomatics-problem-solutions-by-civil-thinking/surveying-levelling-problem-solutions-by-civil-thinking/prepare-a-set-of-profile-leveling-notes-for-the-survey-in-figure-in-addition-to-computing-all-elevations-show-the-arithmetic-check-and-the-resulting-error-in-closure/) - Solution: Below is the solution of this Surveying / Geomatics Eng. problem. You may download the solution: Prepare a set of profile leveling notes for the survey in Figure. In addition to computing all elevations, show the arithmetic check and the resulting error in closureDownload the Solution - [Water at 15°C(ρ=999.1 kg/m³ and μ=1.138x10⁻³ kg/m.s) is flowing steadily in a 30-m-long and 5-cm-diameter horizontal pipe made of stainless steel at a rate of 9 L/s/ Determine (a) the pressure drop, (b) the head loss, and (c) the pumping power requirement to overcome this pressure drop.](https://civilthinking.com/qna/fluid-mechanics/pipe-flow-problem-solutions/turbulent-pipe-flow-problem-solutions/water-at-15cρ999-1-kg-m³-and-μ1-138x10⁻³-kg-m-s-is-flowing-steadily-in-a-30-m-long-and-5-cm-diameter-horizontal-pipe-made-of-stainless-steel-at-a-rate-of-9-l-s-d/) - Solution: Below is the solution of this turbulent pipe flow problem. You may download the solution: water_flow_pressure_drop_head_loss_pumping_power_calculation_15C_30m_5cm_pipe_9LpsDownload the Solution - [Find the support reactions in the following beam carrying two uniformly varying loads and a uniformly distributed load:](https://civilthinking.com/qna/statics/beam-analysis-statics/support-reactions-in-beams/find-the-support-reactions-in-the-following-beam-carrying-two-uniformly-varying-loads-and-a-uniformly-distributed-load/) - Solution: Below is the solution of this beam. You may download the solution: Find the support reactions in the following beam carrying two uniformly varying loads and a uniformly distributed loadDownload the Solution - [Determine the distribution of shear forces and bending moments in a flexural beam for concentrated moment, M=10kN.m at its center. Take length of beam, L=1m.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/determine-the-distribution-of-shear-forces-and-bending-moments-in-a-flexural-beam-for-concentrated-moment-m10kn-m-at-its-center-take-length-of-beam-l1m/) - Solution: Below is the Shear and Moment distribution diagrams of the given beam. You may download the solution: Determine the distribution of shear forces and bending moments in a flexural beam for concentrated moment, M10kN.m at its center. Take length of beam, L1mDownload the Solution - [Determine the distribution of shear forces and bending moments in a flexural beam for distributed force q=10kN/m. Take length of beam, L=1m](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/determine-the-distribution-of-shear-forces-and-bending-moments-in-a-flexural-beam-for-distributed-force-q10kn-m-take-length-of-beam-l1m/) - Solution: Below is the Shear distribution and Moment distribution of this SSB. You may download the solution: Determine the distribution of shear forces and bending moments in a flexural beam for distributed force q10kNm. Take length of beam, L1mDownload the Solution - [Draw the Shear and Moment Diagram of the simply supported beam carrying a point force F=10kN at the center. Take total length of beam, L=1m.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/draw-the-shear-and-moment-diagram-of-the-simply-supported-beam-carrying-a-point-force-f10kn-at-the-center-take-total-length-of-beam-l1m/) - Solution: Below is the SFD and BMD of the given SSB. You may download the solution: Draw the Shear and Moment Diagram of the simply supported beam carrying a point force F10kN at the center. Take total length of beam, L1mDownload the Solution - [Draw the Shear and Moment diagram of the cantilever beam carrying a concentrated moment, M=10kNm at the free end. Take length L=1m](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/draw-the-shear-and-moment-diagram-of-the-cantilever-beam-carrying-a-concentrated-moment-m10knm-at-the-free-end-take-length-l1m/) - Solution: Below is the SFD and BMD diagrams of this cantilever beam. You may download the solution Draw the Shear and Moment diagram of the cantilever beam carrying a concentrated moment, M10kNm at the free end. Take length L1mDownload the solution - [Draw Shear and Moment Diagram of the cantilever beam given, carrying a uniformly distributed load of q=10kN/m, take length L=1m](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/draw-shear-and-moment-diagram-of-the-cantilever-beam-given-carrying-a-uniformly-distributed-load-of-q10kn-m-take-length-l1m/) - Solution: Below is the SFD and BMD of this cantilever beam. You may download the solution: Draw Shear and Moment Diagram of the cantilever beam given, carrying a uniformly distributed load of q 10kNm, take length L 1mDownload the Solution - [Draw Shear and Moment distribution of the given cantilever beam with point load at free end =F = 10kN. Length, L=1m.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/draw-shear-and-moment-distribution-of-the-given-cantilever-beam-with-point-load-at-free-end-f-10kn-length-l1m/) - Solution: Below is the Shear and Moment Diagram of this Cantilever problem. You may download the solution Problem solution draw shear and moment diagram of cantilever beam with point load at free endDownload the solution - [Problem 3: For the shaft shown in the figure, make diagrams of Torque and Shear Stresses for torsion, also determine the total twist angle of the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/problem-3-for-the-shaft-shown-in-the-figure-make-diagrams-of-torque-and-shear-stresses-for-torsion-also-determine-the-total-twist-angle-of-the-shaft/) - Solution: Below is the solution of this Torque Distribution Diagram question. You may download the solution Solid Mechanics Torsion in Shaft Torque distribution diagram and shear stress diagram question solutionDownload the Solution - [For the shaft shown in the figure, make diagram of Torque and shear stresses for torsion, also determine the total twist angle of the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/for-the-shaft-shown-in-the-figure-make-diagram-of-torque-and-shear-stresses-for-torsion-also-determine-the-total-twist-angle-of-the-shaft/) - Solution: Below is the solution of this Solid Mechanics Shaft Torque Distribution Diagram problem. You may download the Solution: Torque distribution diagram and shear stress diagram of shafts problem 2 solutionDownload the Solution - [Determine the maximum torque that can be applied to shaft with diameter d and length l, at which the angle of twist will be 5 degrees. For calculations, assume Kirchhoff's modulus=85Gpa.](https://civilthinking.com/qna/strength-of-materials/shafts/determine-the-maximum-torque-that-can-be-applied-to-shaft-with-diameter-d-and-length-l-at-which-the-angle-of-twist-will-be-5-degrees-for-calculations-assume-kirchhoffs-modulus85gpa/) - Solution: Below is the solution of this Solid Mechanics Shaft problem. You may download the solution: Maximum_Torque_For_Solid_Shaft_With_Diameter_d_And_Length_l_At_5_Degree_Angle_Of_Twist_Assuming_Kirchhoff_Modulus_Of_Rigidity_85GPaDownload the Solution - [Calculate the maximum value of the torque T which can be applied to the shaft shown in the figure below](https://civilthinking.com/qna/strength-of-materials/shafts/calculate-the-maximum-value-of-the-torque-t-which-can-be-applied-to-the-shaft-shown-in-the-figure-below/) - Solution: Below is the Solution of this Solid Mechanics Shaft problem. You may download the Solution Calculate the maximum value of the torque T which can be applied to the shaft shownDownload the Solution - [Problem 4: Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l=4m, b=20mm, F=5000N and E=210Gpa for the following case:](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/problem-4-draw-a-graph-of-tensile-or-compressive-forces-and-stresses-and-calculate-the-total-deformation-of-a-square-steel-bar-with-the-given-data-l4m-b20mm-f5000n-and-e210gpa-for-the-following/) - Solution: Below is the Solution of this Solid Mechanics problem. You may download the solution: Prob4 Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l 4m b 20mm F 5000NDownload the Solution - [Problem 3: Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l=4m, b=20mm, F=5000N and E=210Gpa for the following case:](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/problem-3-draw-a-graph-of-tensile-or-compressive-forces-and-stresses-and-calculate-the-total-deformation-of-a-square-steel-bar-with-the-given-data-l4m-b20mm-f5000n-and-e210gpa-for-the-following/) - Solution: Below is the Solution of this Solid Mechanics problem. You may download the solution: Prob3 Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l 4m b 20mm F 5000NDownload the Solution - [Problem 2: Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data: l=4m, b=20mm, F=5000N and E=210Gpa for the following case:](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/problem-2-draw-a-graph-of-tensile-or-compressive-forces-and-stresses-and-calculate-the-total-deformation-of-a-square-steel-bar-with-the-given-data-l4m-b20mm-f5000n-and-e210gpa-for-the-followin/) - Solution: Below is the solution of this Solid Mechanics problem. You may download the solution Prob2 Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l 4m b 20mm F 5000NDownload the solution - [Problem 1: Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l=4m, b=20mm, F=5000N and E=210Gpa for the following case](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/problem-1-draw-a-graph-of-tensile-or-compressive-forces-and-stresses-and-calculate-the-total-deformation-of-a-square-steel-bar-with-the-given-data-l4m-b20mm-f5000n-and-e210gpa-for-the-following/) - Solution: Below is the solution of this Solid Mechanics problem. You may download the solution: Prob1 Draw a graph of tensile or compressive forces and stresses and calculate the total deformation of a square steel bar with the given data l 4m b 20mm F 5000NDownload the solution - [Calculate the total deformation due to gravity of a homogeneous rod with length l, made of material with density ρ and young's modulus E.](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/calculate-the-total-deformation-due-to-gravity-of-a-homogeneous-rod-with-length-l-made-of-material-with-density-ρ-and-youngs-modulus-e/) - Solution: Below is the Solution of this Solid Mechanics problem. You may download the solution Calculate the total deformation due to gravity of a homogeneous rod with length l, made of material with density ρ and young's modulus EDownload the Solution - [Calculate the tensile stress , total deformation and relative strain of a Dural bar Of length l=5m and diameter d=5mm tensioned by a force F=1000N. Young modulus for Dural is E=72GPa](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/calculate-the-tensile-stress-total-deformation-and-relative-strain-of-a-dural-bar-of-length-l5m-and-diameter-d5mm-tensioned-by-a-force-f1000n-young-modulus-for-dural-is-e72gpa/) - Solution: Below is the solution of this Strength of Materials/ Solid Mechanics problem. You may download the solution Calculate the tensile stress , total deformation and relative strain of a Dural bar Of length l 5m and diameter d 5mm tensioned by a force F 1000N. Young moDownload the Solution - [Find the Area, Centroid, Second Moment of Area, Polar Second moment of Area, Product moment of Area and Principal Axes of the I section given, using Integration method only](https://civilthinking.com/qna/strength-of-materials/moment-of-inertia-problem-solutions/find-the-area-centroid-second-moment-of-area-polar-second-moment-of-area-product-moment-of-area-and-principal-axes-of-the-i-section-given-using-integration-method-only/) - Solution: Below is the solution of this problem. You may download the solution Find the Area, Centroid, Second Moment of Area, Polar Second moment of Area, Product moment of Area and Principal Axes of the I section integrationDownload the solution - [Find the Area, Centroid, Second Moment of Area, Polar Second moment of Area, Product moment of Area and Principal Axes of the inverted T section given, using integration method.](https://civilthinking.com/qna/strength-of-materials/moment-of-inertia-problem-solutions/find-the-area-centroid-second-moment-of-area-polar-second-moment-of-area-product-moment-of-area-and-principal-axes-of-the-inverted-t-section-given-using-integration-method/) - Solution: Below is the solution of this problem. You may download the Solution Find the Area, Centroid, Second Moment of Area, Polar Second moment of Area, Product moment of Area and Principal Axes of the T section integrationDownload the solution - [Oil with a viscosity of 0,6x10-4  m2/s is delivered from a pump to a lubricated sliding surface through a tube with a  diameter d 0,01m and a length l 6m. For what pressure difference will a volume flow rate of 50 cm^3/s  be provided?](https://civilthinking.com/qna/fluid-mechanics/hydrodynamics-problem-solutions/oil-with-a-viscosity-of-06x10-4-m2-s-is-delivered-from-a-pump-to-a-lubricated-sliding-surface-through-a-tube-with-a-diameter-d-001m-and-a-length-l-6m-for-what-pressure-difference-will-a/) - Solution: Below is the solution of this problem. You may download or view the solution Oil with a viscosity of is delivered from a pump to a lubricated sliding surface through a tube witDownload the Solution - [Determine the flow rate QV of water using a Venturi nozzle with dimensions D 100mm, d 50mm inserted into a horizontal pipe through which water flows, if the pressure difference between the inlet to the nozzle and the throat is H = 50mm.](https://civilthinking.com/qna/fluid-mechanics/hydrodynamics-problem-solutions/determine-the-flow-rate-qv-of-water-using-a-venturi-nozzle-with-dimensions-d-100mm-d-50mm-inserted-into-a-horizontal-pipe-through-which-water-flows-if-the-pressure-difference-between-the-inlet-to-th/) - Solution: Below is the solution of this problem. You may download or view the solution Determine the flow rate QV of water using a Venturi nozzle inserted into a horizontal pipe through which water flowsDownload the Solution - [ At what velocity does water flow out of the depicted cylinder through the openings B and C if the force acting on the piston is F = 1500N? How far does the piston move within a minute if the cross-sectional area of each opening is A = 3mm2? Assume a contraction coefficient of ß 0.8.](https://civilthinking.com/qna/fluid-mechanics/hydrodynamics-problem-solutions/at-what-velocity-does-water-flow-out-of-the-depicted-cylinder-through-the-openings-b-and-c-if-the-force-acting-on-the-piston-is-f-1500n-how-far-does-the-piston-move-within-a-minute-if-the-cro/) - Solution: Below is the Solution of this Fluid dynamics problem. you may download or view the solution At what velocity does water flow out of the depicted cylinder through the openings B and C if the force acting on the piston is 1500NDownload the solution - [Find the flow velocity, u of water in the pipe if the difference in total pressure head, measured by a Pitot tube, and static pressure head is H = 500mmH20.](https://civilthinking.com/qna/fluid-mechanics/hydrodynamics-problem-solutions/find-the-flow-velocity-u-of-water-in-the-pipe-if-the-difference-in-total-pressure-head-measured-by-a-pitot-tube-and-static-pressure-head-is-h-500mmh20/) - Solution: Below is the solution of this fluid mechanics problem. You may download or view the solution Find the flow velocity u of water in the pipe if the difference in total pressure head, measured by a Pitot tube, and static pressure head is 500mmH20Download the solution - [A hydraulic cylinder with a piston diameter of D = 80 mm and a piston stroke of s = 500 mm is completely filled with oil. How much will the displacement of the piston be if an external force of F = 30 kN acts on the piston rod? The compressibility coefficient of oil is 56x10¯5mm2/N.](https://civilthinking.com/qna/fluid-mechanics/compression-and-expansion-in-fluids/a-hydraulic-cylinder-with-a-piston-diameter-of-d-80-mm-and-a-piston-stroke-of-s-500-mm-is-completely-filled-with-oil-how-much-will-the-displacement-of-the-piston-be-if-an-external-force-of-f-30/) - Solution: Below is the Solution of this Fluid Mechanics problem. You may download or view the solution A hydraulic cylinder with a piston diameter 80 mm and a piston stroke 500 mm is completely filled with oil. How much will the displacement of the piston be if an external force 30 kN actsDownload the solution - [The tube for measuring acceleration (accelerometer) has been placed on the vehicle. What is the instantaneous acceleration of the vehicle if the levels of the liquid menisci are as shown in the diagram? What is the maximum acceleration that can be measured by this device without losing liquid?](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/the-tube-for-measuring-acceleration-accelerometer-has-been-placed-on-the-vehicle-what-is-the-instantaneous-acceleration-of-the-vehicle-if-the-levels-of-the-liquid-menisci-are-as-shown-in-the-diagra/) - Solution: Below is the Solution of this Fluid Mechanics problem. You may download or view the solution The tube for measuring acceleration (accelerometer) has been placed on the vehicle. What is the instantaneous acceleration of the vehicle if the levels of the liquid menisciDownload the Solution - [Water was poured into a vessel in the shape of an inverted cone with a height H = 1m up to half of its capacity. Calculate the hydrostatic pressure at the lowest point inside the vessel.](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/water-was-poured-into-a-vessel-in-the-shape-of-an-inverted-cone-with-a-height-h-1m-up-to-half-of-its-capacity-calculate-the-hydrostatic-pressure-at-the-lowest-point-inside-the-vessel/) - Solution: Below is the Solution of this Fluid Mechanics problem. You may download or view the solution Water was poured into a vessel in the shape of an inverted cone with a height H = 1m up to half of its capacity. Calculate the hydrostatic pressure at the lowest point inside the vesselDownload the Solution - [A non-deformable pressure vessel of V1 = O,10m3 volume filled completely with methyl alcohol was heated from temperature T1 = 273K to temperature T2 = 323K. Calculate the pressure increase in the vessel.](https://civilthinking.com/qna/fluid-mechanics/compression-and-expansion-in-fluids/a-non-deformable-pressure-vessel-of-v1-o10m3-volume-filled-completely-with-methyl-alcohol-was-heated-from-temperature-t1-273k-to-temperature-t2-323k-calculate-the-pressure-increase-in-the-vess/) - Solution: Below is the Solution of this Fluid Mechanics problem. You may download or view the solution A non-deformable pressure vessel of V1 = O,10m3 volume filled completely with methyl alcohol was heated from temperature T1 = 273K to temperature T2 = 323K. Calculate the pressure increase in the vessel.Download this Solution - [A spherical pressure vessel with a diameter d1 = 1 m was completely filled with methyl alcohol at a 288 K. Calculate the volume of alcohol with which to fill the tank additionally so that the relative pressure in the tank increases to 10 MPa.](https://civilthinking.com/qna/fluid-mechanics/compression-and-expansion-in-fluids/a-spherical-pressure-vessel-with-a-diameter-d1-1-m-was-completely-filled-with-methyl-alcohol-at-a-288-k-calculate-the-volume-of-alcohol-with-which-to-fill-the-tank-additionally-so-that-the-relative/) - Solution: Below is the Solution of this Fluid Mechanics problem. You may download or view the solution A spherical pressure vessel with a diameter dl equals 1 m was completely filled with methyl alcohol at a 288KDownload this Solution - [Python programming to draw Shear and Moment diagrams of a simply supported Beam carrying a uniformly distributed load](https://civilthinking.com/tutorials/python-for-civil-and-structural-engineers/python-programming-to-draw-shear-and-moment-diagrams-of-a-simply-supported-beam-carrying-a-uniformly-distributed-load/) - Below is the Python code to draw Shear and Moment Diagram of this simply supported beam carrying uniformly distributed load: import numpy as np import matplotlib.pyplot as plt l=5 #m q=20 #kN/m x= np.linspace(0,l,200) #SFD V=q*(l/2-x) M=q/2*(l*x-x**2) print(V) print(M) plt.plot(x,V) plt.axhline(0, color='k') plt.fill_between(x, V,0) plt.title("Shear Force Diagram(SFD)") plt.xlabel("x(m)") plt.ylabel("V(kN)") i_zero=np.argmin(np.abs(V)) plt.plot(x[i_zero],V[i_zero], 'ro') plt.text(x[i_zero],V[i_zero]+3,round(x[i_zero],1)) #BMD plt.figure() - [Theory of Errors in Observations](https://civilthinking.com/tutorials/surveying-tutorials/theory-of-errors-in-observations/) - Theory of Errors in Observations Surveyors use measurements to map land and build structures. But no matter how skilled they are or how good the tools, every measurement has some error. Understanding these errors helps surveyors pick the right tools and methods so mistakes stay small enough to not harm their work. Direct and Indirect - [A prismatic steel bar of 75 mm x 75 mm square cross section is subjected to a tensile load P = 600 KN (see figure). Determine the normal and shear stresses on all faces of an element rotated through an angle 45 degree.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/a-prismatic-steel-bar-of-75-mm-x-75-mm-square-cross-section-is-subjected-to-a-tensile-load-p-600-kn-see-figure-determine-the-normal-and-shear-stresses-on-all-faces-of-an-element-rotated-through-a/) - Solution: Below is the solution of this Plane Stress Transformation problem. You may download the Solution. A prismatic steel bar of 75mm x 75mm square cross section is subjected to a tensil load PDownload the Solution - [A 25 mm diameter steel rod (E = 200 GPa) must carry a load in tension of 134 kN (see figure). If the initial length of the stressed portion of the rod is 0.55 m, what is its final length?](https://civilthinking.com/qna/strength-of-materials/axial-stress-problem-solutions/a-25-mm-diameter-steel-rod-e-200-gpa-must-carry-a-load-in-tension-of-134-kn-see-figure-if-the-initial-length-of-the-stressed-portion-of-the-rod-is-0-55-m-what-is-its-final-length/) - Solution: Below is the Solution of this Strength of Materials Problem. You may download the Solution: A 25mm diamter steel rod E is 200Gpa must carry a load in tension of 134knDownload the Solution - [Question: The bond between reinforcing bars and concrete is tested by means of a "pull-out test" of a bar embedded in concrete (see figure). A tensile force p is applied to the end of the bar, which has diameter d and embedment length L. If P=18 kN, d=12 mm, and 300 mm, what average shear stress is developed between the steel and concrete?](https://civilthinking.com/qna/strength-of-materials/shear-stress-question-solutions/question-the-bond-between-reinforcing-bars-and-concrete-is-tested-by-means-of-a-pull-out-test-of-a-bar-embedded-in-concrete-see-figure-a-tensile-force-p-is-applied-to-the-end-of-the-bar-which/) - Solution: Below is the Solution of this Shear Stress Problem. You may download the Solution. BondBetweenRebarsAndConcretePullOutTestP18kNd12mmL300mmDownload the Solution - [Module 2: Units, Significant Figures, and Field Notes](https://civilthinking.com/tutorials/surveying-tutorials/module-2-units-significant-figures-and-field-notes/) - Units of Measurement in Surveying In surveying, we use specific units for length, area, volume, and angle. Two main systems are in use: the English System (feet, inches) and the International System of Units (SI) (meters, centimeters). English System (Foot) The basic unit of length is the foot (ft). Historically there were two definitions: Pre-1959 - [Surveying Field Notes Form Blank pages (both left and right)](https://civilthinking.com/tutorials/surveying-tutorials/surveying-field-notes-blank-pages-both-left-and-right/) - Download the Field Notes Form in Image Format (.png) (Recommended) Surveying field notes form blank both pagesDownload the Surveying Field Notes Form Blank (PDF) - [The 500-kg engine is suspended from the crane boom in Fig. 1—5a. Determine the resultant internal loadings acting on the cross section of the boom at point E.](https://civilthinking.com/qna/strength-of-materials/beams/internal-loading-in-beams/the-500-kg-engine-is-suspended-from-the-crane-boom-in-fig-1-5a-determine-the-resultant-internal-loadings-acting-on-the-cross-section-of-the-boom-at-point-e/) - Solution: Below is the solution of this mechanics of materials problem. You may download the solution The 500-kg engine is suspended from the crane boom in Fig. 15aDownload the solution - [Determine the resultant internal loading acting on the cross section at C of cantilevered beam shown](https://civilthinking.com/qna/strength-of-materials/beams/internal-loading-in-beams/determine-the-resultant-internal-loading-acting-on-the-cross-section-at-c-of-cantilevered-beam-shown/) - Solution: Below is the solution of this mechanics of materials question. You may download the solution determine the resultant internal loading acting on the cross section at C of cantilevered beam shownDownload the Solution - [Quiz on Introduction to Surveying](https://civilthinking.com/tutorials/surveying-tutorials/quiz-on-introduction-to-surveying/) - Surveying Quiz Surveying Quiz Time: 00:00 Start Exam Show Score - [Module 1: Introduction to Surveying](https://civilthinking.com/tutorials/surveying-tutorials/introduction-to-surveying/) - Definition of Surveying Surveying, now commonly known as Geomatics, is the art and science of figuring out the positions of different points either above, on, or below the surface of the Earth. It also involves setting up these points where they are needed. Simple Explanation: Think of surveying like drawing an accurate map. It helps - [Centroid of Composite Area Calculator](https://civilthinking.com/tools/strength-of-materials-tools/centroid-of-composite-area-calculator/) - Step-by-Step Guide: How to Use the Centroid Calculator Follow these steps carefully to find the centroid of any composite 2D shape—even if it has holes or curves. This calculator is built to give you flexibility and accuracy! Step 1: Choose Your Reference Axes Select two edges of your composite shape (commonly the bottom and left - [*6–52. Determine the moment M that should be applied to the beam in order to create a compressive stress at point D of  30Mpa. Also sketch the stress distribution acting over the cross section and compute the maximum stress developed in the beam.](https://civilthinking.com/qna/strength-of-materials/bending-stress-question-solutions/6-52-determine-the-moment-m-that-should-be-applied-to-the-beam-in-order-to-create-a-compressive-stress-at-point-d-of-30mpa-also-sketch-the-stress-distribution-acting-over-the-cross-se/) - Solution: Below is the Solution of this Bending Stress Question. You may download the Solution. 6–52. Determine the moment M that should be applied to the beam in order to create a compressive stress at point. Determine the moment M that should be applied to the beamDownload the Solution - [Plane Stress Transformation online Calculator](https://civilthinking.com/tools/strength-of-materials-tools/plane-stress-transformation-online-calculator/) - Reset 🔄 Solve Plane Stress Transformation problems with Our Free Calculator Our Plane Stress Transformation Calculator is designed for students and professionals in Strength of Materials, Mechanics of Materials, and Statics. Unlike other sites that charge for full solutions or extra features, our tool is 100% free, providing instant, accurate stress transformation results with full - [Solve for member forces AC, BC, and BD in the truss shown using only one section cut (Ritter method)](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/solve-for-member-forces-ac-bc-and-bd-in-the-truss-shown-using-only-one-section-cut-ritter-method/) - Solution: Below is the Solution of this Truss Question Solve for member forces AC, BC, and BD in the truss shown using only one section cut (Ritter method)Download the Solution - [Determine the forces in the members BC BG HG in the truss shown using Ritter method](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/determine-the-forces-in-the-members-bc-bg-hg-in-the-truss-shown-using-ritter-method/) - Solution: Below is the Solution of this Truss Question. You may download the Solution. Determine the forces in the memebrs BC BG HG in the truss shown using Ritter methodDownload the Solution - [Using the method of joints, determine the force in each member of the truss shown in the drawings below. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/using-the-method-of-joints-determine-the-force-in-each-member-of-the-truss-shown-in-the-drawings-below-summarize-the-results-on-a-force-summation-diagram-and-indicate-whether-each-member-is-in-tens-3/) - Solution: Below is the Solution of this Truss Question. You may download the Solution 3 Using the method of joints, determine the force in each member of the truss shown in the drawings below. Summarize the results on a force summation diagramber is in tension or compressionDownload the Solution - [Using the method of joints, determine the force in each member of the truss shown in the drawings below. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/using-the-method-of-joints-determine-the-force-in-each-member-of-the-truss-shown-in-the-drawings-below-summarize-the-results-on-a-force-summation-diagram-and-indicate-whether-each-member-is-in-tens-2/) - Solution: Below is the Solution of this Truss Question. You may download the Solution 2 Using the method of joints, determine the force in each member of the truss shown in the drawings below. Summarize the results on a forceDownload the Solution - [Using the method of joints, determine the force in each member of the truss shown in the drawings below. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/using-the-method-of-joints-determine-the-force-in-each-member-of-the-truss-shown-in-the-drawings-below-summarize-the-results-on-a-force-summation-diagram-and-indicate-whether-each-member-is-in-tens/) - Solution: Below is the Solution of this Truss Question. You may download the solution Using the method of joints, determine the force in each member of the truss shown in the drawings below. Summarize the results on a forceDownload the Solution - [Find the member forces BC and BE in the truss using Ritter's Method](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/find-the-member-forces-bc-and-be-in-the-truss-using-ritters-method/) - Solution: Below is the Solution of this Truss Question. You may download the Solution Find memeber forces in the Truss shown using Ritter MethodDownload the Solution - [A compound beam supports two vertical loads as shown. Determine the support reactions developed at A, B, and E, and also the internal constraint forces at C and D](https://civilthinking.com/qna/strength-of-materials/beams/a-compound-beam-supports-two-vertical-loads-as-shown-determine-the-support-reactions-developed-at-a-b-and-e-and-also-the-internal-constraint-forces-at-c-and-d/) - Solution: Below is the Solution of this question on finding support reactions in compound Beams. You may download the Solution A compound beam supports two vertical loads as shown. Determine the support reactions developed at A, B, and E, and also the internal constraintDownload the Solution - [Determine the resisting moment at the base of the utility pole assuming forces T1=200 and T2=300 are as shown. What are the horizontal reactions RAx and RAy at the base?](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/determine-the-resisting-moment-at-the-base-of-the-utility-pole-assuming-forces-t1200-and-t2300-are-as-shown-what-are-the-horizontal-reactions-rax-and-ray-at-the-base/) - Solution: Below is the solution of this question on finding support reactions. You can download the Solution Determine the resisting moment at the base of the utility pole assuming forces T1=200 and T2=300 are as shown. What are the horizontal reactionsDownload the Solution - [Determine the support reactions for the truss at joints A and D](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/determine-the-support-reactions-for-the-truss-at-joints-a-and-d/) - Solution: Below is the solution of this truss question. You can download the solution Determine the support reactions for the truss at joints A and DDownload - [Draw a free body diagram of member ABD of the Truss shown. Solve for support reactions at A and the tension in cable BC](https://civilthinking.com/qna/strength-of-materials/truss-analysis-in-strength-of-materials-qna/draw-a-free-body-diagram-of-member-abd-of-the-truss-shown-solve-for-support-reactions-at-a-and-the-tension-in-cable-bc/) - Solution: Below is the solution of this truss question. You can download the Solution Draw free body diagram of Truss member ABD. Solve for support reactions at A and the tension in cable BCDownload - [Find the location and magnitude of in-plane major and minor principal stresses](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/find-the-location-and-magnitude-of-in-plane-major-and-minor-principal-stresses/) - Solution: Below is the Solution of this question. You can download the Solution Find the location and magnitude of in-plane major and minor principal stressesDownload the Solution - [Determine the stress components acting on the inclined plane AB using  Stress Transformation Equations](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/determine-the-stress-components-acting-on-the-inclined-plane-ab-using-stress-transformation-equations/) - Solution: Below is the Solution of this problem. You can download the Solution Determine the stress components acting on the inclined plane AB using Stress Transformation EquationsDownload the Solution - [9-13. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9. 1](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-13-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-equilibrium-described-in-sec-9-1/) - Solution: Below is the solution of this Question. You can download the Solution 9-13. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9. 1Download the Solution - [*9–12. Determine the equivalent state of stress on an element at the same point oriented 60° counterclockwise with respect to the element shown. Sketch the results on the element.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-12-determine-the-equivalent-state-of-stress-on-an-element-at-the-same-point-oriented-60-counterclockwise-with-respect-to-the-element-shown-sketch-the-results-on-the-element/) - Solution: Below is the solution of this problem. You can download the solution 9-12. Determine the equivalent state of stress on an element at the same point oriented 60 counterclockwise with respect to the element shownDownload the Solution - [9-11. Determine the equivalent state of stress on an element at the same point oriented 60° clockwise with respect to the element shown. Sketch the results on the element](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-11-determine-the-equivalent-state-of-stress-on-an-element-at-the-same-point-oriented-60-clockwise-with-respect-to-the-element-shown-sketch-the-results-on-the-element/) - Solution: Below is the Solution of this question. You can download the Solution 9-11. Determine the equivalent state of stress on an element at the same point oriented 60° clockwise with respect to the element shown. Sketch the results on the elementDownload the Solution - [Determine the stress components acting on the inclined plane AB. Solve the problem using the method of STRESS TRANSFORMATION EQUATIONS. Draw the sketch](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-stress-transformation-equations-draw-the-sketch/) - Solution: Below is the solution of this question. You can download the solution: Determine the stress components acting on the inclined plane AB. Solve the problem using the method of STRESS TRANSFORMATION EQUATIONS. Draw the sketchDownload the solution - [The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the Stress Transformation equations. Show the result on a sketch.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/the-state-of-stress-at-a-point-in-a-member-is-shown-on-the-element-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-stress-transformation-equations-show-t/) - Solution: Below is the solution of this question. You can download the solution. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the Stress Transformation equationsDownload the Solution - [9-7. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-7-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-equilibrium-described-in-sec-9-1/) - Solution: Below is the Solution of this question. You can download the solution. 9-7. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibriumDownload the Solution - [9-6. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-6-the-state-of-stress-at-a-point-in-a-member-is-shown-on-the-element-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-equilibrium-described-in/) - Solution: Below is the Solution of this question. You can download the solution. 9-6. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibriumDownload the solution - [*9–4. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-4-the-state-of-stress-at-a-point-in-a-member-is-shown-on-the-element-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-equilibrium-des/) - Solution: Below is the solution of this problem. You can download the Solution 9-4. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibriumDownload the solution - [9–3. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-3-the-state-of-stress-at-a-point-in-a-member-is-shown-on-the-element-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-equilibrium-desc/) - Solution: Below is the Solution of this problem. You can download the solution 9–3. The state of stress at a point in a member is shown on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibriumDownload - [Question: Determine the horizontal and vertical components of force which the pin at C exerts on member BC of the frame in Fig. a.](https://civilthinking.com/qna/statics/frames-and-machines-static-analysis-problem-solution/question-determine-the-horizontal-and-vertical-components-of-force-which-the-pin-at-c-exerts-on-member-bc-of-the-frame-in-fig-a/) - Solution: here is the solution of this problem. You can download the solution Determine the horizontal and vertical components of force which the pin at C exerts on member BC of the frame in Fig. aDownload - [Determine the tension in the cables and also the force P required to support the 600-N force using the frictionless pulley system shown in Fig.a.](https://civilthinking.com/qna/statics/frames-and-machines-static-analysis-problem-solution/determine-the-tension-in-the-cables-and-also-the-force-p-required-to-support-the-600-n-force-using-the-frictionless-pulley-system-shown-in-fig-a/) - Solution Here is the solution of this problem. You can download the solution. Determine the tension in the cables and also the force P required to support the 600-N force using the frictionless pulley system shown in Fig.aDownload - [6–17. If the maximum force that any member can support is 8 kN in tension and 6 kN in compression, determine the maximum force P that can be supported at joint D.](https://civilthinking.com/qna/statics/truss-analysis/truss-analysis-by-method-of-joints/6-17-if-the-maximum-force-that-any-member-can-support-is-8-kn-in-tension-and-6-kn-in-compression-determine-the-maximum-force-p-that-can-be-supported-at-joint-d/) - Solution: Below is the solution of this question. You can download the solution 6–17. If the maximum force that any member can support is 8 kN in tension and 6 kN in compression, determine the maximum force P that can be supported at joint DDownload - [9–2. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1.](https://civilthinking.com/qna/strength-of-materials/plane-stress-transformation/9-2-determine-the-stress-components-acting-on-the-inclined-plane-ab-solve-the-problem-using-the-method-of-equilibrium-described-in-sec-9-1/) - Solution: Below is the Solution of this problem. You can download the solution 9–2. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1Download - [A compound beam with internal hinges is loaded as shown. Draw the load, shear, and moment diagrams of the figure show. F=6000N, q=1000N/m.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/a-compound-beam-with-internal-hinges-is-loaded-as-shown-draw-the-load-shear-and-moment-diagrams-of-the-figure-show-f6000n-q1000n-m/) - Solution: Below is the solution of this problem. You can download the solution A compound beam with internal hinges is loaded as shown. Draw the load, shear, and moment diagrams of the figure show. F=6000N, q=1000NmDownload - [The diagram shows a bearing load on a spread footing. Draw the load, shear, and moment diagrams of the figure shown. F=2000N, q=500N/m.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/the-diagram-shows-a-bearing-load-on-a-spread-footing-draw-the-load-shear-and-moment-diagrams-of-the-figure-shown-f2000n-q500n-m/) - Solution: Below is the solution of this problem. You can download the solution The diagram shows a bearing load on a spread footing. Draw the load, shear, and moment diagrams of the figure shown. F=2000N, q=500NmDownload - [Draw the load, shear, and moment diagrams for an overhang beam with a triangular and uniform load. q=6000N/m](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/draw-the-load-shear-and-moment-diagrams-for-an-overhang-beam-with-a-triangular-and-uniform-load-q6000n-m/) - Solution: Below is the solution of this problem. You can download the solution Draw the load, shear, and moment diagrams for an overhang beam with a triangular and unifrom laod q=6000NmDownload - [For a cantilever beam with an upturned end, draw the load, shear, and moment diagrams. F1=4000N, F2=2500N.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/for-a-cantilever-beam-with-an-upturned-end-draw-the-load-shear-and-moment-diagrams-f14000n-f22500n/) - Solution: Below is the solution of this problem. You can download the solution Draw the load, shear and moment diagrams for a cantilever beam with an upturned endDownload - [Draw the load, shear, and moment diagrams for the illustrated single overhang beam with a uniform and concentrated load. (Note: Single overhangs develop two points of possible Mmax ). F=1200N, q=200N/m](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/draw-the-load-shear-and-moment-diagrams-for-the-illustrated-single-overhang-beam-with-a-uniform-and-concentrated-load-note-single-overhangs-develop-two-points-of-possible-mmax-f1200n-q200n/) - Solution: Below is the solution of this problem. You can download the solution Draw the load, shear, and moment diagrams for the overhang beamDownload - [Chapter 9: Stress Transformation concepts](https://civilthinking.com/tutorials/strength-of-materials-tutorials/stress-transformation-concepts/) - Chapter: Stress Transformation CHAPTER OBJECTIVES In this chapter, we will learn how to transform the stress components that are connected with one coordinate system into components associated with a different orientation. This is important because by understanding these transformation equations, you can find out the maximum normal stress and maximum shear stress at a specific - [Soil Mechanics, Chapter-1 Composition and Particle Sizes of Soils](https://civilthinking.com/tutorials/soil-mechanics-book/soil-mechanics-chapter-1-composition-and-particle-sizes-of-soils/) - 1.1 INTRODUCTION In this section, we learn that soils are not just simple dirt – they are complex, natural materials made up of many different components. This chapter sets the stage by explaining that soils come in various compositions and have particles of different sizes, which play a big role in how strong the soil - [Geology: Earthquake Hazards](https://civilthinking.com/tutorials/geology/geology-earthquake-hazards/) - The Great Cascadia Earthquake and Tsunami Pacific Northwest Native American oral traditions all refer to a large flood not too long ago. Locations over 1000 km apart in Japan have records of flooding in January of 1700. The “Orphan Tsunami” since no local landslide was felt Tsunami travel times for Cascadia: Using tsunami arrival times - [Structural Geology](https://civilthinking.com/tutorials/geology/structural-geology/) - Structural Geology: How Rocks Deform The earth’s crust changes shape due to the applied stress Measuring the orientation of structures •Dip: direction and angle that a bed or plane is inclined from horizontal True dip is only observed in cross-section if that section is vertical and parallel to the dip direction: Reverse Faults Hanging Wall - [Metamorphism in Geology](https://civilthinking.com/tutorials/geology/metamorphism-in-geology/) - Metamorphic Rocks Engineering properties •T, P, composition changes à metamorphic rocks •Again – variable in properties à strength •foliated rocks •planes of weakness along foliation •strength: depends on directions of stress (slate to schist) •gneiss: interlocking xls & limited foliation •massive (nonfoliated) •quartzite, hornfels – very strong •marble: large interlocking xls, but weak à - [Sedimentary Rocks Geology](https://civilthinking.com/tutorials/geology/sedimentary-rocks-geology/) - Sedimentary Rocks and Processes Ripples Ripple Symmetry: a paleo-current indicator Ringold Formation ripples, White Bluffs, WA Lithified Mudcracks Mudcracks in a rock suggest that the rock’s environment of deposition was sometimes wet (when the mud would form), but also sometimes dry (when the mud would crack). Examples: flood plains, mud flats, dry lake beds MUD - [Volcanic Processes and Hazards](https://civilthinking.com/tutorials/geology/volcanic-processes-and-hazards/) - Volcanic Processes and Hazards Volcanic Eruption Styles: The primary control on Eruption style is GAS CONTENT and VISCOSITY of the magma Viscosity controls some features of Lava Transport Viscosity is defined as the resistance to flow in a fluid: μ=τ/ε (= stress/strain rate) viscosity affects: Rate of travel of lava flows Dome Stability and Collapse Thickness - [Structural Dynamics Concepts](https://civilthinking.com/tutorials/structural-dynamics/structural-dynamics-concepts/) - Depending on the nature of the impact on the structure, loads are divided into static and dynamic. Loads are considered static if they change very slowly (with an infinitely small increment in time), without jolts or impacts. Dynamic loads are those that can change their magnitude, direction or position in relatively short periods of time. - [Earthquakes](https://civilthinking.com/tutorials/geology/earthquakes/) - What is an Earthquake? An earthquake is the vibration, produced by a rapid release of seismic earth. Caused by accumulation and sudden release of stress in the crust Transmitted in the form of seismic waves Radiates in all directions from its source (the focus, or hypocenter) Instruments around the world record an event by measuring - [5-64. The device serves as a compact torsion spring. It is made of A-36 steel and consists of a solid inner shaft CB which is surrounded by and attached to a tube AB using a rigid ring at B. The ring at A can also be assumed rigid and is fixed from rotating. If the allowable shear stress for the material is Tallow =12 ksi and the angle of twist at C is limited to 30, determine the maximum torque T that can be applied at the end C.](https://civilthinking.com/qna/strength-of-materials/shafts/5-64-the-device-serves-as-a-compact-torsion-spring-it-is-made-of-a-36-steel-and-consists-of-a-solid-inner-shaft-cb-which-is-surrounded-by-and-attached-to-a-tube-ab-using-a-rigid-ring-at-b-the-ring/) - Solution: Below is the solution of this problem. you can download the solution. 5-64. The device serves as a compact torsion spring. It is made of A-36 steel and consists of a solid inner shaft CB which is surrounded by and attached to a tube AB using a rigid ring at BDownload the Solution Get - [5-63. The device serves as a compact torsional spring. It is made of A-36 steel and consists of a solid inner shaft CB which is surrounded by and attached to a tube AB using a rigid ring at B. The ring at A can also be assumed rigid and is fixed from rotating. If a torque of T= 2 kip • in. is applied to the shaft, determine the angle of twist at the end C and the maximum shear stress in the tube and shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-63-the-device-serves-as-a-compact-torsional-spring-it-is-made-of-a-36-steel-and-consists-of-a-solid-inner-shaft-cb-which-is-surrounded-by-and-attached-to-a-tube-ab-using-a-rigid-ring-at-b-the-rin/) - Solution: Below is the solution of this problem. you can download the solution. 5-63. The device serves as a compact torsional spring. It is made of A-36 steel and consists of a solid inner shaft CB which is surrounded by and attached to a tube AB using a rigid ring at BDownload the Solution Get - [5-62. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotation. If the support at D is fixed, determine the angle of twist of end A when the torques are applied to the assembly as shown.](https://civilthinking.com/qna/strength-of-materials/shafts/5-62-the-two-shafts-are-made-of-a-36-steel-each-has-a-diameter-of-1-in-and-they-are-supported-by-bearings-at-a-b-and-c-which-allow-free-rotation-if-the-support-at-d-is-fixed-determine-the-ang/) - Solution: Below is the solution of this problem. you can download the solution. 5-62. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotation. If the support at D is fixedDownload the Solution Get Problem - [•5-61. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotation. If the support at D is fixed, determine the angle of twist of end B when the torques are applied to the assembly as shown.](https://civilthinking.com/qna/strength-of-materials/shafts/5-61-the-two-shafts-are-made-of-a-36-steel-each-has-a-diameter-of-1-in-and-they-are-supported-by-bearings-at-a-b-and-c-which-allow-free-rotation-if-the-support-at-d-is-fixed-determin/) - Solution: Below is the solution of this problem. you can download the solution. 5-61. The two shafts are made of A-36 steel. Each has a diameter of 1 in., and they are supported by bearings at A, B, and C, which allow free rotationDownload the Solution Get Problem Solutions - [*5-60. The shaft is made of A-36 steel. It has a diameter of 1 in. and is supported by bearings at A and D, which allow free rotation. Determine the angle of twist of gear C with respect to B.](https://civilthinking.com/qna/strength-of-materials/shafts/5-60-the-shaft-is-made-of-a-36-steel-it-has-a-diameter-of-1-in-and-is-supported-by-bearings-at-a-and-d-which-allow-free-rotation-determine-the-angle-of-twist-of-gear-c-with-respect-to-b/) - Solution: Below is the solution of this problem. you can download the solution. 5-60. The shaft is made of A-36 steel. It has a diameter of 1 in. and is supported by bearings at A and D, which allow free rotation. Determine the angle of twist of gear C with respect to BDownload the Solution - [5-59. The shaft is made of A-36 steel. It has a diameter of 1 in. and is supported by bearings at A and D, which allow free rotation. Determine the angle of twist of B with respect to D.](https://civilthinking.com/qna/strength-of-materials/shafts/5-59-the-shaft-is-made-of-a-36-steel-it-has-a-diameter-of-1-in-and-is-supported-by-bearings-at-a-and-d-which-allow-free-rotation-determine-the-angle-of-twist-of-b-with-respect-to-d/) - Solution: Below is the solution of this problem. you can download the solution. 5-59. The shaft is made of A-36 steel. It has a diameter of 1 in. and is supported by bearings at A and D, which allow free rotation. Determine the angle of twist of B with respect to DDownload the Solution Get - [5-58. The motor delivers 40 hp to the 304 stainless steel solid shaft while it rotates at 20 Hz. The shaft has a diameter of 1.5 in. and is supported on smooth bearings at A and B, which allow free rotation of the shaft. The gears C and D fixed to the shaft remove 25 hp and 15 hp, respectively. Determine the absolute maximum stress in the shaft and the angle of twist of gear C with respect to gear D.](https://civilthinking.com/qna/strength-of-materials/shafts/5-58-the-motor-delivers-40-hp-to-the-304-stainless-steel-solid-shaft-while-it-rotates-at-20-hz-the-shaft-has-a-diameter-of-1-5-in-and-is-supported-on-smooth-bearings-at-a-and-b-which-allow-free-ro/) - Solution: Below is the solution of this problem. you can download the solution. 5-58. The motor delivers 40 hp to the 304 stainless steel solid shaft while it rotatesDownload Get Problem Solutions - [•5-57. The motor delivers 40 hp to the 304 stainless steel shaft while it rotates at 20 Hz. The shaft is supported on smooth bearings at A and B, which allow free rotation of the shaft. The gears C and D fixed to the shaft remove 25 hp and 15 hp, respectively. Determine the diameter of the shaft to the nearest 1/8 in. if the allowable shear stress is Tallow= 8 ksi and the allowable angle of twist of C with respect to D is 0.2 degree.](https://civilthinking.com/qna/strength-of-materials/shafts/5-57-the-motor-delivers-40-hp-to-the-304-stainless-steel-shaft-while-it-rotates-at-20-hz-the-shaft-is-supported-on-smooth-bearings-at-a-and-b-which-allow-free-rotation-of-the-shaft-the-ge/) - Solution: Below is the solution of this problem. you can download the solution. 5-57. The motor delivers 40 hp to the 304 stainless steel shaft while it rotates at 20 Hz. The shaft is supported on smooth bearings at A and BDownload the Solution Get Problem Solutions - [5-56. The splined ends and gears attached to the A-36 steel shaft are subjected to the torques shown. Determine the angle of twist of end B with respect to end A. The shaft has a diameter of 40 mm.](https://civilthinking.com/qna/strength-of-materials/shafts/5-56-the-splined-ends-and-gears-attached-to-the-a-36-steel-shaft-are-subjected-to-the-torques-shown-determine-the-angle-of-twist-of-end-b-with-respect-to-end-a-the-shaft-has-a-diameter-of-40-mm/) - Solution: Below is the solution of this problem. you can download the solution. 5-56. The splined ends and gears attached to the A-36 steel shaft are subjected to the torques shown. Determine the angle of twist of end B with respect to end A. The shaft has a diameter of 40 mm.Download the Solution Get - [5-55. The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at C. The tube has an outer diameter of 40 mm and wall thickness of 5 mm.](https://civilthinking.com/qna/strength-of-materials/shafts/5-55-the-assembly-is-made-of-a-36-steel-and-consists-of-a-solid-rod-20-mm-in-diameter-fixed-to-the-inside-of-a-tube-using-a-rigid-disk-at-b-determine-the-angle-of-twist-at-c-the-tube-has-an-outer-d/) - Solution: Below is the solution of this problem. you can download the solution. 5-55. The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at CDownload the Solution Get Problem - [5-54. The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at D. The tube has an outer diameter of 40 mm and wall thickness of 5 mm.](https://civilthinking.com/qna/strength-of-materials/shafts/5-54-the-assembly-is-made-of-a-36-steel-and-consists-of-a-solid-rod-20-mm-in-diameter-fixed-to-the-inside-of-a-tube-using-a-rigid-disk-at-b-determine-the-angle-of-twist-at-d-the-tube-has-an-outer-d/) - Solution: Below is the solution of this problem. you can download the solution. 5-54. The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at DDownload the Solution Get Problem - [•5—53. The 20-mm-diameter A-36 steel shaft is subjected to the torques shown. Determine the angle of twist of the end B.](https://civilthinking.com/qna/strength-of-materials/shafts/5-53-the-20-mm-diameter-a-36-steel-shaft-is-subjected-to-the-torques-shown-determine-the-angle-of-twist-of-the-end-b/) - Solution: Below is the solution of this problem. you can download the solution. 5-53. The 20-mm-diameter A-36 steel shaft is subjected to the torques shown. Determine the angle of twist of the end B.Download the Solution Get Problem Solutions - [*5-52. The engine of the helicopter is delivering 600 hp to the rotor shaft AB when the blade is rotating at 1200 rev/min. Determine to the nearest 1/8 in. the diameter of the shaft AB if the allowable shear stress is Tallow =10.5 ksi and the vibrations limit the angle of twist of the shaft to 0.05 rad. The shaft is 2 ft long and made from L2 steel.](https://civilthinking.com/qna/strength-of-materials/shafts/5-52-the-engine-of-the-helicopter-is-delivering-600-hp-to-the-rotor-shaft-ab-when-the-blade-is-rotating-at-1200-rev-min-determine-to-the-nearest-1-8-in-the-diameter-of-the-shaft-ab-if-the-allowabl/) - Solution: Below is the solution of this problem. you can download the solution. 5-52. The engine of the helicopter is delivering 600 hp to the rotor shaft AB when the blade is rotating at 1200 rpm. Determine to the nearest. Shear stress is 10.5 ksiDownload the Solution Get Problem Solutions - [5-51. The engine of the helicopter is delivering 600 hp to the rotor shaft AB when the blade is rotating at 1200 rev/min. Determine to the nearest 1/8 in. the diameter of the shaft AB if the allowable shear stress is Tallow = 8 ksi and the vibrations limit the angle of twist of the shaft to 0.05 rad. The shaft is 2 ft long and made from L2 steel.](https://civilthinking.com/qna/strength-of-materials/shafts/5-51-the-engine-of-the-helicopter-is-delivering-600-hp-to-the-rotor-shaft-ab-when-the-blade-is-rotating-at-1200-rev-min-determine-to-the-nearest-1-8-in-the-diameter-of-the-shaft-ab-if-the-allowable/) - Solution: Below is the solution of this problem. you can download the solution. 5-51. The engine of the helicopter is delivering 600 hp to the rotor shaft AB when the blade is rotating at 1200 rpm. Determine to the nearest 1over8 inchDownload the Solution Get Problem Solutions - [5-50. The hydrofoil boat has an A-36 steel propeller shaft that is 100 ft long. It is connected to an in-line diesel engine that delivers a maximum power of 2500 hp and causes the shaft to rotate at 1700 rpm. If the outer diameter of the shaft is 8 in. and the wall thickness is -g in., determine the maximum shear stress developed in the shaft. Also, what is the "wind up," or angle of twist in the shaft at full power?](https://civilthinking.com/qna/strength-of-materials/shafts/5-50-the-hydrofoil-boat-has-an-a-36-steel-propeller-shaft-that-is-100-ft-long-it-is-connected-to-an-in-line-diesel-engine-that-delivers-a-maximum-power-of-2500-hp-and-causes-the-shaft-to-rotate-at-1/) - Solution: Below is the solution of this problem. you can download the solution. 5-50. The hydrofoil boat has an A-36 steel propeller shaft that is 100 ft long. It is connected to an in-line dieselDownload Get Problem Solutions - [5-49. The A-36 steel axle is made from tubes AB and CD and a solid section BC. It is supported on smooth bearings that allow it to rotate freely. If the gears, fixed to its ends, are subjected to 85-N•m torques, determine the angle of twist of gear A relative to gear D. The tubes have an outer diameter of 30 mm and an inner diameter of 20 mm. The solid section has a diameter of 40 mm.](https://civilthinking.com/qna/strength-of-materials/shafts/05-49-the-a-36-steel-axle-is-made-from-tubes-ab-and-cd-and-a-solid-section-bc-it-is-supported-on-smooth-bearings-that-allow-it-to-rotate-freely-if-the-gears-fixed-to-its-ends-are-subjected-to-85/) - Solution: Below is the solution of this problem. you can download the solution. 05-49. The A-36 steel axle is made from tubes AB and CD and a solid section BC. It is supported on smooth bearings that allow it to rotate freely. If the gears, fixed to its ends, are subjected to 85Download Get Problem - [*5-48. A shaft is subjected to a torque T. Compare the effectiveness of using the tube shown in the figure with that of a solid section of radius c. To do this, compute the percent increase in torsional stress and angle of twist per unit length for the tube versus the solid section.](https://civilthinking.com/qna/strength-of-materials/shafts/5-48-a-shaft-is-subjected-to-a-torque-t-compare-the-effectiveness-of-using-the-tube-shown-in-the-figure-with-that-of-a-solid-section-of-radius-c-to-do-this-compute-the-percent-increase-in-torsion/) - Solution: Below is the solution of this problem. you can download the solution. 5-48. A shaft is subjected to a torque T. Compare the effectiveness of using the tube shown in the figure with that of a solid section of radius c. To do this, compute the percentDownload Get Problem Solutions - [5-47. The propellers of a ship are connected to a A-36 steel shaft that is 60 m long and has an outer diameter of 340 mm and inner diameter of 260 mm. If the power output is 4.5 MW when the shaft rotates at 20 rad/s, determine the maximum torsional stress in the shaft and its angle of twist.](https://civilthinking.com/qna/strength-of-materials/shafts/5-47-the-propellers-of-a-ship-are-connected-to-a-a-36-steel-shaft-that-is-60-m-long-and-has-an-outer-diameter-of-340-mm-and-inner-diameter-of-260-mm-if-the-power-output-is-4-5-mw-when-the-shaft-rota/) - Solution: Below is the solution of this problem. you can download the solution. 5-47. The propellers of a ship are connected to a A-36 steel shaft that is 60 m long and has an outer diameter of 340 mm and inner diameter of 260 mmDownload Get Problem Solutions - [5-46. The motor delivers 15 hp to the pulley at A while turning at a constant rate of 1800 rpm. Determine to the nearest 1/8 in. the smallest diameter of shaft BC if the allowable shear stress for steel is Tallow= 12 ksi. The belt does not slip on the pulley.](https://civilthinking.com/qna/strength-of-materials/shafts/5-46-the-motor-delivers-15-hp-to-the-pulley-at-a-while-turning-at-a-constant-rate-of-1800-rpm-determine-to-the-nearest-1-8-in-the-smallest-diameter-of-shaft-bc-if-the-nearest-8-allowable-shear-stre/) - Solution: Below is the solution of this problem. you can download the solution. 5-46. The motor delivers 15 hp to the pulley at A while turning at a constant rate of 1800 rpm. Determine to the nearest 1over8 inDownload Get Problem Solutions - [*5-44. The drive shaft AB of an automobile is made of a steel having an allowable shear stress of Tallow = 8 ksi. If the outer diameter of the shaft is 2.5 in. and the engine delivers 200 hp to the shaft when it is turning at 1140 rev/min, determine the minimum required thickness of the shaft's wall.](https://civilthinking.com/qna/strength-of-materials/shafts/5-44-the-drive-shaft-ab-of-an-automobile-is-made-of-a-steel-having-an-allowable-shear-stress-of-tallow-8-ksi-if-the-outer-diameter-of-the-shaft-is-2-5-in-and-the-engine-delivers-200-hp-to-the-sh/) - Solution: Below is the solution of this problem. you can download the solution. 5-44. The drive shaft AB of an automobile is made of a steel having an allowable shear stress of Tallow = 8 ksiDownload Get Problem Solutions - [5-43. A steel tube having an outer diameter of 2.5 in. is used to transmit 35 hp when turning at 2700 rev/min. Determine the inner diameter d of the tube to the nearest in. if the allowable shear stress is Tallow 10 ksi.](https://civilthinking.com/qna/strength-of-materials/shafts/5-43-a-steel-tube-having-an-outer-diameter-of-2-5-in-is-used-to-transmit-35-hp-when-turning-at-2700-rev-min-determine-the-inner-diameter-d-of-the-tube-to-the-nearest-in-if-the-allowable-shear-stre/) - Solution: Below is the solution of this problem. you can download the solution. 5-43. A steel tube having an outer diameter of 2.5 in. is used to transmit 35 hp when turning at 2700 rpm. Determine the inner diameter dDownload Get Problem Solutions - [5-42. The A-36 solid tubular steel shaft is 2 m long and has an outer diameter of 60 mm. It is required to transmit 60 kW of power from the motor M to the pump P. Determine the smallest angular velocity the shaft can have if the allowable shear stress is Tallow = 80 MPa.](https://civilthinking.com/qna/strength-of-materials/shafts/5-42-the-a-36-solid-tubular-steel-shaft-is-2-m-long-and-has-an-outer-diameter-of-60-mm-it-is-required-to-transmit-60-kw-of-power-from-the-motor-m-to-the-pump-p-determine-the-smallest-angular-veloci/) - Solution: Below is the solution of this problem. you can download the solution. 5-42. The A-36 solid tubular steel shaft is 2 m long and has an outer diameter of 60 mm. It is required to transmit 60 kW of powerDownload Get Problem Solutions - [•5-41. The A-36 steel tubular shaft is 2 m long and has an outer diameter of 50 mm. When it is rotating at 40 rad/s, it transmits 25 kW of power from the motor M to the pump P. Determine the smallest thickness of the tube if the allowable shear stress is Tallow 80 MPa.](https://civilthinking.com/qna/strength-of-materials/shafts/5-41-the-a-36-steel-tubular-shaft-is-2-m-long-and-has-an-outer-diameter-of-50-mm-when-it-is-rotating-at-40-rad-s-it-transmits-25-kw-of-power-from-the-motor-m-to-the-pump-p-determine-the-s/) - Solution: Below is the solution of this problem. you can download the solution. 5-41. The A-36 steel tubular shaft is 2 m long and has an outer diameter of 50 mm. When it is rotating at 40rpsDownload Get Problem Solutions - [*5-40. Determine the absolute maximum shear stress developed in the shaft in Prob. 5-39.](https://civilthinking.com/qna/strength-of-materials/shafts/5-40-determine-the-absolute-maximum-shear-stress-developed-in-the-shaft-in-prob-5-39/) - For your reference, here is the problem 5-39: 5-39. The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaft while it is turning at 50 rev/s. If - [5-39. The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaft while it is turning at 50 rev/s. If gears A, B, and C remove 3 kW, 4 kW, and 5 kW respectively, determine the maximum shear stress developed in the shaft within regions CF and BC. The shaft is free to turn in its support bearings D and E.](https://civilthinking.com/qna/strength-of-materials/shafts/5-39-the-solid-steel-shaft-df-has-a-diameter-of-25-mm-and-is-supported-by-smooth-bearings-at-d-and-e-it-is-coupled-to-a-motor-at-f-which-delivers-12-kw-of-power-to-the-shaft-while-it-is-turning-at/) - Solution: Below is the solution of this problem. you can download the solution. 5-39. The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaftDownload Get Problem Solutions - [5-38. The motor A develops a power of 300 W and turns its connected pulley at 90 rev/min. Determine the required diameters of the steel shafts on the pulleys at A and B if the allowable shear stress is Tallow=85 Mpa.](https://civilthinking.com/qna/strength-of-materials/shafts/5-38-the-motor-a-develops-a-power-of-300-w-and-turns-its-connected-pulley-at-90-rev-min-determine-the-required-diameters-of-the-steel-shafts-on-the-pulleys-at-a-and-b-if-the-allowable-shear-stress-i/) - Solution: Below is the solution of this problem. you can download the solution. 5-38. The motor A develops a power of 300 W and turns its connected pulley at 90 rpm. Determine the required diameters of the steel shaftsDownload Get Problem Solutions - [•5-37. A ship has a propeller drive shaft that is turning at 1500 rev/min while developing 1800 hp. If it is 8 ft long and has a diameter of 4 in., determine the maximum shear stress in the shaft caused by torsion.](https://civilthinking.com/qna/strength-of-materials/shafts/5-37-a-ship-has-a-propeller-drive-shaft-that-is-turning-at-1500-rev-min-while-developing-1800-hp-if-it-is-8-ft-long-and-has-a-diameter-of-4-in-determine-the-maximum-shear-stress-in-the-sh/) - Solution: Below is the solution of this problem. you can download the solution. 5-37. A ship has a propeller drive shaft that is turning at 1500 rpm while developing 1800 hp. If it is 8 ft long and has a diameter of 4 inDownload Get Problem Solutions - [5-36. The drive shaft of the motor is made of a material having an allowable shear stress of Tallow 75 MPa. If the outer diameter of the tubular shaft is 20 mm and the wall thickness is 2.5 mm, determine the maximum allowable power that can be supplied to the motor when the shaft is operating at an angular velocity of 1500 rev/min.](https://civilthinking.com/qna/strength-of-materials/shafts/5-36-the-drive-shaft-of-the-motor-is-made-of-a-material-having-an-allowable-shear-stress-of-tallow-75-mpa-if-the-outerdiameter-of-the-tubular-shaft-is-20-mm-and-the-wall-thickness-is-2-5-mm-determi/) - Solution: Below is the solution of this problem. you can download the solution. 5-36. The drive shaft of the motor is made of a material having an allowable shear stress of Tallow 75 MPa. If the outer diameter of the tubular shaft is 20 mmDownload Get Problem Solutions - [6-6. Draw the shear and moment diagrams for the overhang beam.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/6-6-draw-the-shear-and-moment-diagrams-for-the-overhang-beam/) - Solution: Below is the solution of this problem. you can download the solution. 6-6. Draw the shear and moment diagrams for the overhang beam.Download Get Problem Solutions - [6-5. Draw the shear and moment diagrams for the beam.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/6-5-draw-the-shear-and-moment-diagrams-for-the-beam/) - Solution: Below is the solution of this problem. you can download the solution. 6-5. Draw the shear and moment diagrams for the beam.Download Get Problem Solutions - [6-2. Draw the shear and moment diagrams for the simply supported beam.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/6-2-draw-the-shear-and-moment-diagrams-for-the-simply-supported-beam/) - Solution: Below is the solution of this problem. you can download the solution. 6-2. Draw the shear and moment diagrams for the simply supported beam.Download Get Problem Solutions - [6-3. The engine crane is used to support the engine, which has a weight of 1200 lb. Draw the shear and moment diagrams of the boom ABC when it is in the horizontal position shown.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/6-3-the-engine-crane-is-used-to-support-the-engine-which-has-a-weight-of-1200-lb-draw-the-shear-and-moment-diagrams-of-the-boom-abc-when-it-is-in-the-horizontal-position-shown/) - Solution: Below is the solution of this problem. you can download the solution. 6-3. The engine crane is used to support the engine, which has a weight of 1200 lb. Draw the shDownload Get Problem Solutions - [6-4. Draw the shear and moment diagrams for the cantilever beam.](https://civilthinking.com/qna/strength-of-materials/shear-and-moment-diagrams/6-4-draw-the-shear-and-moment-diagrams-for-the-cantilever-beam/) - Solution: Below is the solution of this problem. you can download the solution. 6-4. Draw the shear and moment diagrams for the cantilever beam.Download Get Problem Solutions - [6-1. Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/6-1-draw-the-shear-and-moment-diagrams-for-the-shaft-the-bearings-at-a-and-b-exert-only-vertical-reactions-on-the-shaft/) - Solution: Below is the solution of this problem. you can download the solution. 6-1. Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft.Download Get Problem Solutions - [5-35. The 25-mm-diameter shaft on the motor is made of a material having an allowable shear stress of 75 MPa. If the motor is operating at its maximum power of 5 kW, determine the minimum allowable rotation of the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-35-the-25-mm-diameter-shaft-on-the-motor-is-made-of-a-material-having-an-allowable-shear-stress-of-75-mpa-if-the-motor-is-operating-at-its-maximum-power-of-5-kw-determine-the-minimum-allowable-ro/) - Solution: Below is the solution of this problem. you can download the solution. 5-35. The 25-mm-diameter shaft on the motor is made of a material having an allowable shear stress of 75 MPa. If the motorDownload Get Problem Solutions - [5-34. The gear motor can develop 3 hp when it turns at 150 rev/min. If the allowable shear stress for the shaft is 12 ksi, determine the smallest diameter of the shaft to the nearest 1/8 inch that can be used.](https://civilthinking.com/qna/strength-of-materials/shafts/5-34-the-gear-motor-can-develop-3-hp-when-it-turns-at-150-rev-min-if-the-allowable-shear-stress-for-the-shaft-is-12-ksi-determine-the-smallest-diameter-of-the-shaft-to-the-nearest-1-8-inch-that-can/) - Solution: Below is the solution of this problem. you can download the solution. 5-34. The gear motor can develop 3 hp when it turns at 150 rpm. If the allowable shear stress for the shaft is 12 ksiDownload Get Problem Solutions - [•5-33. The gear motor can develop 2 hp when it turns at 450 rev/min. If the shaft has a diameter of 1 in., determine the maximum shear stress developed in the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-33-the-gear-motor-can-develop-2-hp-when-it-turns-at-450-rev-min-if-the-shaft-has-a-diameter-of-1-in-determine-the-maximum-shear-stress-developed-in-the-shaft/) - Solution: Below is the solution of this problem. you can download the solution. 5-33. The gear motor can develop 2 hp when it turns at 450 rpm. If the shaft has a diameter of 1 in., determine the maximum shear stress developed in the shaft.Download Solution Get Problem Solutions - [5-32. The pump operates using the motor that has a power of 85 W. If the impeller at B is turning at 150 rev/min, determine the maximum shear stress developed in the 20-mm-diameter transmission shaft at A.](https://civilthinking.com/qna/strength-of-materials/shafts/5-32-the-pump-operates-using-the-motor-that-has-a-power-of-85-w-if-the-impeller-at-b-is-turning-at-150-rev-min-determine-the-maximum-shear-stress-developed-in-the-20-mm-diameter-transmission-shaft/) - Solution: Below is the solution of this problem. you can download the solution. 5-32. The pump operates using the motor that has a power of 85 W. If the impeller at B is turning at 150 rpmDownload Solution Get Problem Solutions - [5-31. The solid steel shaft AC has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at C, which delivers 3 kW of power to the shaft while it is turning at 50 rev/s. If gears A and B remove 1 kW and 2 k W, respectively, determine the maximum shear stress developed in the shaft within regions AB and BC. The shaft is free to turn in its support bearings D and E.](https://civilthinking.com/qna/strength-of-materials/shafts/5-31-the-solid-steel-shaft-ac-has-a-diameter-of-25-mm-and-is-supported-by-smooth-bearings-at-d-and-e-it-is-coupled-to-a-motor-at-c-which-delivers-3-kw-of-power-to-the-shaft-while-it-is-turning-at-5/) - Solution: Below is the solution of this problem. you can download the solution. 5-31. The solid steel shaft AC has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at CDownload Solution Get Problem Solutions - [5-30. The shaft is subjected to a distributed torque along its length of t =(10x^2) N • m/m, where x is in meters. If the maximum stress in the shaft is to remain constant at 80 MPa, determine the required variation of the radius c of the shaft for 0< x <3 m.](https://civilthinking.com/qna/strength-of-materials/shafts/5-30-the-shaft-is-subjected-to-a-distributed-torque-along-its-length-of-t-10x2-n-m-m-where-x-is-in-meters-if-the-maximum-stress-in-the-shaft-is-to-remain-constant-at-80-mpa-determine/) - Solution: Below is the solution of this problem. you can download the solution. 5-30. The shaft is subjected to a distributed torque along its length of tDownload Solution Get Problem Solutions - [5-29. When drilling a well at constant angular velocity, the bottom end of the drill pipe encounters a torsional resistance TA. Also, soil along the sides of the pipe creates a distributed frictional torque along its length, varying uniformly from zero at the surface B to t A at A. Determine the minimum torque TB that must be supplied by the drive unit to overcome the resisting torques, and compute the maximum shear stress in the pipe. The pipe has an outer radius ro and an inner radius ri.](https://civilthinking.com/qna/strength-of-materials/shafts/5-29-when-drilling-a-well-at-constant-angular-velocity-the-bottom-end-of-the-drill-pipe-encounters-a-torsional-resistance-ta-also-soil-along-the-sides-of-the-pipe-creates-a-distributed-frictional/) - Solution: Below is the solution of this problem. you can download the solution. 5-29. When drilling a well at constant angular velocity, the bottom end of the drill pipe encounters a torsional resistance TADownload Get Problem Solutions - [*5-28. The A-36 steel shaft is supported on smooth bearings that allow it to rotate freely. If the gears are subjected to the torques shown, determine the required diameter of the shaft to the nearest mm if Tallow =60 MPa.](https://civilthinking.com/qna/strength-of-materials/shafts/5-28-the-a-36-steel-shaft-is-supported-on-smooth-bearings-that-allow-it-to-rotate-freely-if-the-gears-are-subjected-to-the-torques-shown-determine-the-required-diameter-of-the-shaft-to-the-nearest/) - Solution: Below is the solution of this problem. you can download the solution. 5-28. The A-36 steel shaft is supported on smooth bearings that allow it to rotate freely. If the gears are subjected to the torques shownDownload Get Problem Solutions - [5-27. The A-36 steel shaft is supported on smooth bearings that allow it to rotate freely. If the gears are subjected to the torques shown, determine the maximum shear stress developed in the segments AB and BC. The shaft has a diameter of 40 mm.](https://civilthinking.com/qna/strength-of-materials/shafts/5-27-the-a-36-steel-shaft-is-supported-on-smooth-bearings-that-allow-it-to-rotate-freely-if-the-gears-are-subjected-to-the-torques-shown-determine-the-maximum-shear-stress-developed-in-the-segments/) - Solution: Below is the solution of this problem. you can download the solution. 5-27. The A-36 steel shaft is supported on smooth bearings that allow it to rotate freely. If the gears are subjected to the torques shownDownload Get Problem Solutions - [5-26. A cylindrical spring consists of a rubber annulus bonded to a rigid ring and shaft. If the ring is held fixed and a torque T is applied to the shaft, determine the maximum shear stress in the rubber.](https://civilthinking.com/qna/strength-of-materials/shafts/5-26-a-cylindrical-spring-consists-of-a-rubber-annulus-bonded-to-a-rigid-ring-and-shaft-if-the-ring-is-held-fixed-and-a-torque-t-is-applied-to-the-shaft-determine-the-maximum-shear-stress-in-the-ru/) - Solution: Below is the solution of this problem. you can download the solution. 5-26. A cylindrical spring consists of a rubber annulus bonded to a rigid ring and shaft. If the ring is held fixeDownload Get Problem Solutions - [•5-25. The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall at C and it is subjected to the uniformly distributed torque along its entire length, determine the absolute maximum shear stress in the pipe. Discuss the validity of this result.](https://civilthinking.com/qna/strength-of-materials/shafts/5-25-the-copper-pipe-has-an-outer-diameter-of-2-50-in-and-an-inner-diameter-of-2-30-in-if-it-is-tightly-secured-to-the-wall-at-c-and-it-is-subjected-to-the-uniformly-distributed-torque-alo/) - Solution: Below is the solution of this problem. you can download the solution. 5-25. The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall at CDownload Get Problem Solutions - [5-1. A shaft is made of a steel alloy having an allowable shear stress of Tallow 12 ksi. If the diameter of the shaft is 1.5 in., determine the maximum torque T that can be transmitted. What would be the maximum torque T' if a 1-in.-diameter hole is bored through the shaft? Sketch the](https://civilthinking.com/qna/strength-of-materials/shafts/⚫5-1-a-shaft-is-made-of-a-steel-alloy-having-an-allowable-shear-stress-of-tallow-12-ksi-if-the-diameter-of-the-shaft-is-1-5-in-determine-the-maximum-torque-t-that-can-be-transmitted-wha/) - Solution: Below is the solution of this problem 5-1. A shaft is made of a steel alloy having an allowable shear stress of Tallow 12 ksi. If the diameter of the shaft is 1.5 inDownload Get Problem Solutions - [*5-24. The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall at C and a uniformly distributed torque is applied to it as shown, determine the shear stress developed at points A and B. These points lie on the pipe's outer surface. Sketch the shear stress on volume elements located at A and B.](https://civilthinking.com/qna/strength-of-materials/shafts/5-24-the-copper-pipe-has-an-outer-diameter-of-2-50-in-and-an-inner-diameter-of-2-30-in-if-it-is-tightly-secured-to-the-wall-at-c-and-a-uniformly-distributed-torque-is-applied-to-it-as-show/) - Solution: Below is the solution of this problem. you can download the solution. 5—24. The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in.Download Get Problem Solutions - [5-22. The solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the required diameter d of the shaft to the nearest mm if the allowable shear stress for the material is Tallow = 50 MPa.](https://civilthinking.com/qna/strength-of-materials/shafts/5-22-the-solid-shaft-is-subjected-to-the-distributed-and-concentrated-torsional-loadings-shown-determine-the-required-diameter-d-of-the-shaft-to-the-nearest-mm-if-the-allowable-shear-stress-for-the/) - Solution: Below is the solution of this problem. you can download the solution. 5-22. The solid shaft is subjected to the distributed and concentrated torsional loadings shownDownload the Solution Get Problem Solutions - [•5—21. The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimum shear stresses on the outer surface of the shaft and specify their locations, measured from the fixed end A.](https://civilthinking.com/qna/strength-of-materials/shafts/5-21-the-60-mm-diameter-solid-shaft-is-subjected-to-the-distributed-and-concentrated-torsional-loadings-shown-determine-the-absolute-maximum-and-minimum-shear-stresses-on-the-outer/) - Solution: Below is the solution of this problem. you can download the solution. 5—21. The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown.Download the Solution Get Problem Solutions - [1/1 Determine the angles made by the vector V = −36i + 15j with the positive x- and y-axes. Write the unit vector n in the direction of V.](https://civilthinking.com/qna/statics/force-system/1-1-determine-the-angles-made-by-the-vector-v-−36i-15j-with-the-positive-x-and-y-axes-write-the-unit-vector-n-in-the-direction-of-v/) - Solution: Below is the solution of this problem. you can download the solution. 1 1 Determine the angles made by the vector V −36i 15j with the positive x- and y-axesDownload the Solution Get Problem Solutions - [*5-20. Two wrenches are used to tighten the pipe. If the pipe is made from a material having an allowable shear stress of Tallow = 85 MPa, determine the allowable maximum force P that can be applied to each wrench. The pipe has an outer diameter of 25 mm and inner diameter of 20 mm.](https://civilthinking.com/qna/strength-of-materials/shafts/5-20-two-wrenches-are-used-to-tighten-the-pipe-if-the-pipe-is-made-from-a-material-having-an-allowable-shear-stress-of-tallow-85-mpa-determine-the-allowable-maximum-force-p-that-can-be-applied-t/) - Solution: Below is the solution of this problem. you can download the solution. 5-20. Two wrenches are used to tighten the pipe. If the pipe is made from a material having an allowable shear stress of TallowDownload the Solution Get Problem Solutions - [MATLAB Tutorials by Civil Thinking](https://civilthinking.com/youtube/matlab/matlab-tutorials-by-civil-thinking/) - [5-19. Two wrenches are used to tighten the pipe. If P = 300 N is applied to each wrench, determine the maximum torsional shear stress developed within regions AB and BC. The pipe has an outer diameter of 25 mm and inner diameter of 20 mm. Sketch the shear stress distribution for both cases.](https://civilthinking.com/qna/strength-of-materials/shafts/5-19-two-wrenches-are-used-to-tighten-the-pipe-if-p-300-n-is-applied-to-each-wrench-determine-the-maximum-torsional-shear-stress-developed-within-regions-ab-and-bc-the-pipe-has-an-outer-diameter/) - Solution: Below is the solution of this problem. you can download the solution. 5-19. Two wrenches are used to tighten the pipe. If P = 300 N is applied to each wrenchDownload the Solution Get Problem Solutions - [3-26 The basic barometer can be used to measure the height of a building. If the barometric readings at the top and at the bottom of a building are 730 and 755 mmHg, respectively, determine the height of the building. Assume an average air density of 1.18 kg/m3.](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/3-26-the-basic-barometer-can-be-used-to-measure-the-height-of-a-building-if-the-barometric-readings-at-the-top-and-at-the-bottom-of-a-building-are-730-and-755-mmhg-respectively-determine-the-height/) - Solution: Below is the solution of this problem. you can download the solution. 3-26 The basic barometer can be used to measure the height of a building.Download the Solution Get Problem Solutions - [5-17. The rod has a diameter of 1 in. and a weight of 10 lb/ft. Determine the maximum torsional stress in the rod at a section located at A due to the rod's weight.](https://civilthinking.com/qna/strength-of-materials/shafts/5-17-the-rod-has-a-diameter-of-1-in-and-a-weight-of-10-lb-ft-determine-the-maximum-torsional-stress-in-the-rod-at-a-section-located-at-a-due-to-the-rods-weight/) - Solution: Below is the solution of this problem. you can download the solution. 5-17. The rod has a diameter of 1 in. and a weight of 10 lbft.Download the Solution Get Problem Solutions - [3-15 The absolute pressure in water at a depth of 8 m is read to be 175 kPa. Determine (a) the local atmospheric pressure, and (b) the absolute pressure at a depth of 8 m in a liquid whose specific gravity is 0.78 at the same location.](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/3-15-the-absolute-pressure-in-water-at-a-depth-of-8-m-is-read-to-be-175-kpa-determine-a-the-local-atmospheric-pressure-and-b-the-absolute-pressure-at-a-depth-of-8-m-in-a-liquid-whose-specific-gr/) - Solution: Below is the solution of this problem. you can download the solution. 3-15 The absolute pressure in water at a depth of 8 m is read to be 175 kPaDownload the Solution Get Problem Solutions - [3-12 The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Fig. P3-12. Determine the gage pressure of air in the tank if h1 = 0.4 m, h2 = 0.6 m, and h = 0.8 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively.](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/3-12-the-water-in-a-tank-is-pressurized-by-air-and-the-pressure-is-measured-by-a-multifluid-manometer-as-shown-in-fig-p3-12-determine-the-gage-pressure-of-air-in-the-tank-if-h1-0-4-m-h2-0-6-m/) - Solution: Below is the solution of this problem. you can download the solution. 3-12 The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Fig. P3-12Download the Solution Get Problem Solutions - [3-11E A manometer is used to measure the air pressure in a tank. The fluid used has a specific gravity of 1.25, and the differential height between the two arms of the manometer is 28 in. If the local atmospheric pressure is 12.7 psia, determine the absolute pressure in the tank for the cases of the manometer arm with the (a) higher and (b) lower fluid level being attached to the tank.](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/3-11e-a-manometer-is-used-to-measure-the-air-pressure-in-a-tank-the-fluid-used-has-a-specific-gravity-of-1-25-and-the-differ-ential-height-between-the-two-arms-of-the-manometer-is-28-in-if-the-loc/) - Solution: Below is the solution of this problem. you can download the solution. 3-11E_Manometer_Air_Pressure_SG_1.25_Height_28in_Atmos_12.7psiaDownload the Solution Get Problem Solutions - [3-8 A vacuum gage connected to a chamber reads 36 kPa at a location where the atmospheric pressure is 92 kPa. Determine the absolute pressure in the chamber.](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/3-8-a-vacuum-gage-connected-to-a-chamber-reads-36-kpa-at-a-location-where-the-atmospheric-pressure-is-92-kpa-determine-the-absolute-pressure-in-the-chamber/) - Solution: Below is the solution of this problem. you can download the solution. 3-8 A vacuum gage connected to a chamber reads 36 kPa at a location where the atmospheric pressure is 92 kPa. Determine the absolute pressure in the chamber.Download the Solution Get Problem Solutions - [3-7 The piston of a vertical piston-cylinder device containing a gas has a mass of 40 kg and a cross-sectional area of 0.012 m2 (Fig P3-7). The local atmospheric pressure is 95 kPa, and the gravitational acceleration is 9.81 m/s2. (a) Determine the pressure inside the cylinder. (b) If some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change?](https://civilthinking.com/qna/fluid-mechanics/fluid-statics/3-7-the-piston-of-a-vertical-piston-cylinder-device-containing-a-gas-has-a-mass-of-40-kg-and-a-cross-sectional-area-of-0-012-m2-fig-p3-7-the-local-atmospheric-pressure-is-95-kpa-and-the-gravitatio/) - Solution: Below is the solution of this problem. you can download the solution. 3.7Download the Solution Get Problem Solutions - [5-15. The solid shaft is made of material that has an allowable shear stress of Tallow = 10 MPa. Determine the required diameter of the shaft to the nearest mm.](https://civilthinking.com/qna/strength-of-materials/shafts/5-15-the-solid-shaft-is-made-of-material-that-has-an-allowable-shear-stress-of-tallow-10-mpa-determine-the-required-diameter-of-the-shaft-to-the-nearest-mm/) - Solution: Below is the solution of this problem. you can download the solution. 15Download the Solution Get Problem Solutions - [5-13. If the applied torque on shaft CD is T' = 75 N. m, determine the absolute maximum shear stress in each shaft. The bearings B, C, and D allow free rotation of the shafts, and the motor holds the shafts fixed from rotating.](https://civilthinking.com/qna/strength-of-materials/shafts/5-13-if-the-applied-torque-on-shaft-cd-is-t-75-n-m-determine-the-absolute-maximum-shear-stress-in-each-shaft-the-bearings-b-c-and-d-allow-free-rotation-of-the-shafts-and-the-motor-holds-the-2/) - Solution: Below is the solution of this problem. you can download the solution. 13Download the Solution Get Problem Solutions - [5-14. The solid 50-mm-diameter shaft is used to transmit the torques applied to the gears. Determine the absolute maximum shear stress in the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-13-if-the-applied-torque-on-shaft-cd-is-t-75-n-m-determine-the-absolute-maximum-shear-stress-in-each-shaft-the-bearings-b-c-and-d-allow-free-rotation-of-the-shafts-and-the-motor-holds-the/) - Solution: Below is the solution of this problem. you can download the solution. 14Download the Solution Get Problem Solutions - [5-12. The motor delivers a torque of 50 N. m to the shaft AB. This torque is transmitted to shaft CD using the gears at E and F. Determine the equilibrium torque T' on shaft CD and the maximum shear stress in each shaft. The bearings B, C, and D allow free rotation of the shafts.](https://civilthinking.com/qna/strength-of-materials/shafts/5-12-the-motor-delivers-a-torque-of-50-n-m-to-the-shaft-ab-this-torque-is-transmitted-to-shaft-cd-using-the-gears-at-e-and-f-determine-the-equilibrium-torque-t-on-shaft-cd-and-the-maximum-shear/) - Solution: Below is the solution of this problem. you can download the solution. 12Download the Solution Get Problem Solutions - [5-11. The assembly consists of two sections of galvanized steel pipe connected together using a reducing coupling at B. The smaller pipe has an outer diameter of 0.75 in. and an inner diameter of 0.68 in., whereas the larger pipe has an outer diameter of 1 in. and an inner diameter of 0.86 in. If the pipe is tightly secured to the wall at C, determine the maximum shear stress developed in each section of the pipe when the couple shown is applied to the handles of the wrench.](https://civilthinking.com/qna/strength-of-materials/shafts/5-11-the-assembly-consists-of-two-sections-of-galvanized-steel-pipe-connected-together-using-a-reducing-coupling-at-b-the-smaller-pipe-has-an-outer-diameter-of-0-75-in-and-an-inner-diameter-of-0-68/) - Solution: Below is the solution of this problem. you can download the solution. 11Download the Solution Get Problem Solutions - [5-10. The coupling is used to connect the two shafts together. Assuming that the shear stress in the bolts is uniform, determine the number of bolts necessary to make the maximum shear stress in the shaft equal to the shear stress in the bolts. Each bolt has a diameter d.](https://civilthinking.com/qna/strength-of-materials/shafts/5-10-the-coupling-is-used-to-connect-the-two-shafts-together-assuming-that-the-shear-stress-in-the-bolts-is-uniform-determine-the-number-of-bolts-necessary-to-make-the-maximum-shear-stress-in-the-s/) - Solution: Below is the solution of this problem. you can download the solution. 10Download the Solution Get Problem Solutions - [5-9. The shaft consists of three concentric tubes, each made from the same material and having the inner and outer radii shown. If a torque of T = 800 Nm is applied to the rigid disk fixed to its end, determine the maximum shear stress in the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-9-the-shaft-consists-of-three-concentric-tubes-each-made-from-the-same-material-and-having-the-inner-and-outer-radii-shown-if-a-torque-of-t-800-nm-is-applied-to-the-rigid-disk-fixed-to-its-end/) - Solution: Below is the solution of this problem. you can download the solution. 9Download the Solution Get Problem Solutions - [5-7. The solid shaft has a diameter of 0.75 in. If it is subjected to the torques shown, determine the maximum shear stress developed in regions CD and EF of the shaft. The bearings at A and F allow free rotation of the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-7-the-solid-shaft-has-a-diameter-of-0-75-in-if-it-is-subjected-to-the-torques-shown-determine-the-maximum-shear-stress-developed-in-regions-cd-and-ef-of-the-shaft-the-bearings-at-a-and-f-allow-f/) - Solution: Below is the solution of this problem. you can download the solution. 7Download the Solution Get Problem Solutions - [5-6. The solid shaft has a diameter of 0.75 in. If it is subjected to the torques shown, determine the maximum shear stress developed in regions BC and DE of the shaft. The bearings at A and F allow free rotation of the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-6-the-solid-shaft-has-a-diameter-of-0-75-in-if-it-is-subjected-to-the-torques-shown-determine-the-maximum-shear-stress-developed-in-regions-bc-and-de-of-the-shaft-the-bearings-at-a-and-f-allow-f-2/) - Solution: Below is the solution of this problem. you can download the solution. 6Download the Solution Get Problem Solutions - [5-6. The solid shaft has a diameter of 0.75 in. If it is subjected to the torques shown, determine the maximum shear stress developed in regions BC and DE of the shaft. The bearings at A and F allow free rotation of the shaft.](https://civilthinking.com/qna/strength-of-materials/shafts/5-6-the-solid-shaft-has-a-diameter-of-0-75-in-if-it-is-subjected-to-the-torques-shown-determine-the-maximum-shear-stress-developed-in-regions-bc-and-de-of-the-shaft-the-bearings-at-a-and-f-allow-f/) - Solution: Below is the solution of this problem. you can download the solution. 6Download the Solution Get Problem Solutions - [5-5. The copper pipe has an outer diameter of 40 mm and an inner diameter of 37 mm. If it is tightly secured to the wall at A and three torques are applied to it as shown, determine the absolute maximum shear stress developed in the pipe.](https://civilthinking.com/qna/strength-of-materials/shafts/5-5-the-copper-pipe-has-an-outer-diameter-of-40-mm-and-an-inner-diameter-of-37-mm-if-it-is-tightly-secured-to-the-wall-at-a-and-three-torques-are-applied-to-it-as-shown-determine-the-absolute-maxim/) - Solution: Below is the solution of this problem. you can download the solution. 5Download the Solution Get Problem Solutions - [5-4. The tube is subjected to a torque of 750 N.m. Determine the amount of this torque that is resisted by the gray shaded section. Solve the problem two ways: (a) by using the torsion formula, (b) by finding the resultant of the shear-stress distribution.](https://civilthinking.com/qna/strength-of-materials/shafts/5-4-the-tube-is-subjected-to-a-torque-of-750-n-m-determine-the-amount-of-this-torque-that-is-resisted-by-the-gray-shaded-section-solve-the-problem-two-ways-a-by-using-the-torsion-formula-b-by/) - Solution: Below is the solution of this problem. you can download the solution. 4Download the Solution Get Problem Solutions - [5-3. The solid shaft is fixed to the support at C and subjected to the torsional loadings shown. Determine the shear stress at points A and B and sketch the shear stress on volume elements located at these points.](https://civilthinking.com/qna/strength-of-materials/shafts/5-3-the-solid-shaft-is-fixed-to-the-support-at-c-and-subjected-to-the-torsional-loadings-shown-determine-the-shear-stress-at-points-a-and-b-and-sketch-the-shear-stress-on-volume-elements-located-at/) - Solution: Below is the solution of this problem. you can download the solution. 3Download the Solution Get Problem Solutions - [5-2. The solid shaft of radius r is subjected to a torque T. Determine the radius r' of the inner core of the shaft that resists one-half of the applied torque (T/2). Solve the problem two ways: (a) by using the torsion formula, (b) by finding the resultant of the shear-stress distribution.](https://civilthinking.com/qna/strength-of-materials/shafts/5-2-the-solid-shaft-of-radius-r-is-subjected-to-a-torque-t-determine-the-radius-r-of-the-inner-core-of-the-shaft-that-resists-one-half-of-the-applied-torque-t-2-solve-the-problem-two-ways-a/) - Solution: Below is the solution of this problem 2Download Get Problem Solutions - [SAP2000 Graphic interface](https://civilthinking.com/tutorials/sap2000/sap2000-graphic-interface/) - In this class, we will explore the SAP2000 software, start it, observe how it loads, examine its interface after loading, and cover a few more aspects. Loading Screen: This is how the SAP2000 looks while it's loading: The first window that appears after loading: To begin, click on 'New Model' from the Toolbar or Menu - [Introduction to SAP2000](https://civilthinking.com/tutorials/sap2000/introduction-to-sap2000/) - SAP2000: Introduction SAP2000 is a civil engineering software used for structural analysis and design. In structural analysis and design of civil engineering projects, we analyze structures for their strength under various load cases and design them according to strength requirements. Structural analysis of any civil structure is based on the principles of mechanics, which are - [*6-120. The shaft is supported on two journal bearings at A and B which offer no resistance to axial loading. Determine the required diameter d of the shaft if the allowable bending stress for the material is 150 MPa.](https://civilthinking.com/qna/strength-of-materials/shafts/6-120-the-shaft-is-supported-on-two-journal-bearings-at-a-and-b-which-offer-no-resistance-to-axial-loading-determine-the-required-diameter-d-of-the-shaft-if-the-allowable-bending-stress-for-the-mat/) - View Solution - [STAAD Foundation Advanced Tutorials by Civil Thinking](https://civilthinking.com/youtube/staad-foundation-advanced/staad-foundation-advanced-tutorials-by-civil-thinking/) - [One common assumption when we use the Bernoulli equation is that the velocity at the surface of a large tank or reservoir is zero. In reality, the water level would be going down over time so there probably is a velocity at the water surface. Let's investigate the assumption that v1=0 using the below open tank being drained by a pipe.](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/one-common-assumption-when-we-use-the-bernoulli-equation-is-that-the-velocity-at-the-surface-of-a-large-tank-or-reservoir-is-zero-in-reality-the-water-level-would-be-going-down-over-time-so-there-pr/) - Solution: Get Problem Solutions - [A service main (water pipe) at the end of a street decreases in diameter from 8 inches to 4 inches. The flowrate is 5 ft3/s and the pressure at point 1 is 50 psi. Neglect losses. a. Find the velocity at point 2 in ft/s. b. Calculate the pressure at point 2 in psi. c. Compare the pressure in the wider pipe with the pressure in the narrow pipe. Is it what you would expect?(1)8"-diameter4"-diameter(2)10 ft](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/a-service-main-water-pipe-at-the-end-of-a-street-decreases-in-diameter-from-8-inches-to-4-inches-the-flowrate-is-5-ft3-s-and-the-pressure-at-point-1-is-50-psi-neglect-losses-a-find-the-velocity/) - Solution: Get Problem Solutions - [Henry Pitot originally used the Pitot tube to measure the flow rate in the Seine River. If the height h in the diagram is 21 cm, calculate the velocity in the river.90° bend](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/henry-pitot-originally-used-the-pitot-tube-to-measure-the-flow-rate-in-the-seine-river-if-the-height-h-in-the-diagram-is-21-cm-calculate-the-velocity-in-the-river-90-bend/) - Solution: Get Problem Solutions - [3.7.3 Draw the energy line and hydraulic grade line for the flow shown in Problem 3.6.48.](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-7-3-draw-the-energy-line-and-hydraulic-grade-line-for-the-flow-shown-in-problem-3-6-48/) - Solution: Get Problem Solutions - [3.6.82 WP Water flows through the branching pipe shown in Fig. P3.6.82. If viscous effects are negligible, determine the pressure at section (2) and the pressure at section (3).A3=0.035 m221-1 m3/s23-10 mA1 = 0.1 m2P1 = 300 kPa(3)21=0(1)FIGURE P3.6.82(2)V2-14 m/s A2=0.03 m222=0](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-6-82-wp-water-flows-through-the-branching-pipe-shown-in-fig-p3-6-82-if-viscous-effects-are-negligible-determine-the-pressure-at-section-2-and-the-pressure-at-section-3-a30-035-m221-1-m3-s23/) - Solution: Get Problem Solutions - [3.6.48 WP Water flows steadily with negligible viscous effects through the pipe shown in Fig. P3.6.48. It is known that the 4-in.- diameter section of thin-walled tubing will collapse if the pressure within it becomes less than 10 psi below atmospheric pressure. Deter- mine the maximum value that h can have without causing collapse of the tubing.](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-6-48-wp-water-flows-steadily-with-negligible-viscous-effects-through-the-pipe-shown-in-fig-p3-6-48-it-is-known-that-the-4-in-diameter-section-of-thin-walled-tubing-will-collapse-if-the-pressure/) - Solution: Get Problem Solutions - [3.6.47 WP The specific gravity of the manometer fluid shown in Fig. P3.6.47 is 1.07. Determine the volume flowrate, Q, if the flow is inviscid and incompressible and the flowing fluid is (a) water, (b) gasoline, or (c) air at standard conditions.0.09-m diameter0.05 mT 20 mm10 mmFIGURE P3.6.47](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-6-47-wp-the-specific-gravity-of-the-manometer-fluid-shown-in-fig-p3-6-47-is-1-07-determine-the-volume-flowrate-q-if-the-flow-is-inviscid-and-incompressible-and-the-flowing-fluid-is-a-water-b/) - Bernoulli equation problem solutions - [3.6.13 WP Figure P3.6.13 shows a tube for siphoning water from an aquarium. Determine the rate at which the water leaves the aquarium for the conditions shown. Is there an advantage to having the large- diameter section? The water flow is inviscid.1/4 in. I.D. tubeA = 6 ft2FIGURE P3.6.13h=5 ft](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-6-13-wp-figure-p3-6-13-shows-a-tube-for-siphoning-water-from-an-aquarium-determine-the-rate-at-which-the-water-leaves-the-aquarium-for-the-conditions-shown-is-there-an-advantage-to-having-the-larg/) - Solution: Get Problem Solutions - [3.6.9 WP Water flows from a pressurized tank, through a 6-in.-diameter pipe, exits from a 2-in-diameter nozzle, and rises 20 ft above the nozzle, as shown in Fig. P3.6.9. Determine the pressure in the tank if the flow is steady, frictionless, and incom- pressible.20 ftAir+2 in.2 ft16 in.FIGURE P3.6.9](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-6-9-wp-water-flows-from-a-pressurized-tank-through-a-6-in-diameter-pipe-exits-from-a-2-in-diameter-nozzle-and-rises-20-ft-above-the-nozzle-as-shown-in-fig-p3-6-9-determine-the-pressure-in-the/) - Bernoulli equation problem solutions - [3.5.8 WP 2013 Indianapolis 500 champion Tony Kanaan holds his hand out of his IndyCar while driving through still air with standard atmospheric conditions. (a) For safety, the pit lane speed limit is 60 mph. At this speed, what is the maximum pressure on his hand? (b) Back on the race track, what is the maximum pressure when he is driving his IndyCar at 225 mph? (c) On the straightaways, the IndyCar reaches speeds in excess of 235 mph. For this speed, is your solution method for parts (a) and (b) reasonable? Explain.](https://civilthinking.com/tutorials/fluid-dynamics/bernoulli-equation-problem-solutions/3-5-8-wp-2013-indianapolis-500-champion-tony-kanaan-holds-his-hand-out-of-his-indycar-while-driving-through-still-air-with-standard-atmospheric-conditions-a-for-safety-the-pit-lane-speed-limit-is/) - Solution: Get Problem Solutions - [Ansys Youtube Tutorials by Civil Thinking](https://civilthinking.com/youtube/ansys/ansys-youtube-tutorials-by-civil-thinking/) ## Pages - [Civil Thinking](https://civilthinking.com/) - Civil Engineering Simulations and Online Tutoring - [Get Problem Solutions](https://civilthinking.com/getproblemsolutions/) - [Book online Class](https://civilthinking.com/book-online-class/) - Need online tutoring in Civil Engineering? Book the online class with us using the form.We teach Students Globally, from all the countries. 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