Civil Thinking › Beam Analysis Problems Simply Supported Beam with Point Load

Problem Statement

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

Concentrated Loads:
• 10 kN downward at x = 0.5 m

Required:
• Determine the support reactions
• Draw the Shear Force Diagram (SFD)
• Draw the Bending Moment Diagram (BMD)

Equilibrium equation ∑M = 0 Expanded form − P1·0.5 + R2y·1 = 0 Substitution − 10 kN×0.5 m + 5 kN×1 m = 0 Solved reaction

Equilibrium equation ∑Fy = 0 Expanded form − P1 + R1y + R2y = 0 Substitution − 10 kN + 5 kN + 5 kN = 0 Solved reaction

ΣFy check − 10 kN + 5 kN + 5 kN = 0 = 0 ΣM check − 10 kN×0.5 m + 5 kN×1 m = 0 = 0

Position (m)	Shear (kN)	Remark
0	5	Start of beam
0.5	0	Zero shear location
0.5	5	Just before point load / reaction
0.5	-5	Just after point load / reaction
1	-5	End of beam
1	-5	Just before point load / reaction
1	0	Just after point load / reaction

s = 0
(5) × 0 = 0
ΣM = 0

s = 0.5
(5) × 0.5 = -2.5
(-10) × 0 = 0
ΣM = -2.5

s = 1
(5) × 1 = -5
(5) × 0 = 0
(-10) × 0.5 = 5
ΣM = 0