Civil Thinking › Beam Analysis Problems Loaded Beam under Distributed Loading

Problem Statement

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

Distributed Loads:
• 1 kN/m acting from x = 0 to 1 m

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

Equilibrium equation ∑M = 0 Expanded form − W1·0.5 + R2y·1 = 0 Substitution − 1 kN×0.5 m + 0.5 kN×1 m = 0 Solved reaction

Equilibrium equation ∑Fy = 0 Expanded form − W1 + R1y + R2y = 0 Substitution − 1 kN + 0.5 kN + 0.5 kN = 0 Solved reaction

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

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

s = 0
(0.5) × 0 = 0
ΣM = 0

s = 0.5
(0.5) × 0.5 = -0.25
0.125 (UDL resultant)
ΣM = -0.125

s = 1
(0.5) × 1 = -0.5
(0.5) × 0 = 0
0.5 (UDL resultant)
ΣM = 0