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Problem 3 · MMD August 2021
Beam on a flat bed
A beam of mass 61.162 kg and length 10 m rests completely on a flat support. A concentrated mass of 30.581 kg is placed on the centre of the beam. Draw the SF and BM diagrams to scale.
- A continuous rigid bed provides a uniform upward reaction equal to total weight / length.
- Self-weight is cancelled by part of that bed reaction; only the concentrated mass produces net SF and BM.
Loading diagram
g = 9.81 m/s². 61.162 × 9.81 = 600 N, 30.581 × 9.81 = 300 N.
Max sagging BM
375 N·m
at 5 m
SF and BM diagrams
x5 m|SF -150|BM 375
Drag across the plots to read values. Sagging BM is drawn positive.
Step 1
Convert mass to force
Beam = 61.162 × 9.81 = 600 N. Concentrated mass = 30.581 × 9.81 = 300 N. Total 900 N.
Step 2
Bed reaction
Uniform upward reaction = 900/10 = 90 N/m. Beam self-weight = 60 N/m down. Net UDL = 30 N/m up, plus 300 N down at mid-span.
Step 3
Diagrams
SF runs +30x to +150 N just left of centre, jumps −300 N to −150 N, then back to 0 at B. BM is a pair of parabolas meeting at 375 N·m (sagging) at mid-span.