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Problem 5 · MMD November 2017
Symbolic simply-supported UDL
A beam of length ℓ and weight w per unit length is supported at its ends. Draw SF and BM diagrams of the beam.
- Classic result. The numeric diagram below uses ℓ = 10 m and w = 2 kN/m so the shapes are readable; change them in Studio.
Loading diagram
R1
10 kN
0 m from A
R2
10 kN
10 m from A
Max sagging BM
25 kN·m
at 5 m
SF and BM diagrams
x5 m|SF 0|BM 25
Drag across the plots to read values. Sagging BM is drawn positive.
Step 1
Reactions
Total load = wℓ. Symmetric, so RA = RB = wℓ/2.
Step 2
Shear
SF(x) = wℓ/2 − w x. Straight line from +wℓ/2 at A to −wℓ/2 at B. Zero at mid-span.
Step 3
Bending moment
BM(x) = (w x / 2)(ℓ − x), a parabola. Zero at the ends. Maximum sagging BM = wℓ²/8 at x = ℓ/2.