All problems
Problem 7 · MMD April 2021
Uniform log, 2 m stations
A uniform log AB is 10 m long, weighs 100 kN. It is supported at a point 2 m from end A. It also carries a point load of 30 kN at end B. Draw SF and BM diagrams of the beam stating their values at intervals of 2 metres.
- A single knife edge cannot hold this loading (the combined centre of gravity sits 6.15 m from A). The second support is taken 2 m from B — the usual MMD overhang arrangement, leaving B free to carry the 30 kN load.
Loading diagram
R1
40 kN
2 m from A
R2
90 kN
8 m from A
Max sagging BM
0 kN·m
at 0 m
Max hogging BM
-80 kN·m
at 8 m
SF and BM diagrams
x5 m|SF -10|BM -5
Drag across the plots to read values. Sagging BM is drawn positive.
Step 1
Reactions
w = 10 kN/m. Supports C at 2 m and D at 8 m. ΣV = 130 kN. Moments about C: 100×3 + 30×8 = 540 = RD×6, so RD = 90 kN and RC = 40 kN.
Step 2
Two-metre stations
Evaluate SF (left and right of jumps) and BM at 0, 2, 4, 6, 8 and 10 m. SF is zero at 4 m; the largest hogging BM is −80 kN·m at D.