Answer: C. the beam has a constant bending moment (M₀) throughout
Every section has only the couple M₀ on its free-end side, so the bending moment is M₀ everywhere (pure bending).
Question 18Easy
A 2 m cantilever carries point loads of 300 N, 500 N and 800 N at 0.5 m, 1.2 m and 2 m from the fixed end. The shear force (N) at the fixed end and bending moment (N·m) at the free end are:
Beyond mid-span lies half the loaded length (L/6): V = wL/6. At the fixed end the whole load w·L/3 acts: V = wL/3.
Question 21Easy
A simply supported beam of length L carries two point loads, each P, at one-third of the span from either end. The bending moment at the left end support is:
No transverse force acts anywhere, so the sum of vertical forces on either side of any section is zero.
Question 25Easy
For a simply supported beam, if the area under the shear force diagram between two points is a constant C, the difference between the bending moments at these points is:
dM/dx = V, so M₂ − M₁ = ∫V dx = area of the SFD between the points = C.
Question 26Hard
A UDL of 10 kN/m and 5 m length moves from the left to the right support of a simply supported beam of span 10 m. The maximum bending moment at 4 m from the left support is:
Place the load so the section divides it in the ratio 4 : 6 (2 m left, 3 m right of the section). R_A = 27.5 kN; M = 27.5 × 4 − 10 × 2 × 1 = 90 kN·m. The book key gives (a) 70 kN·m; the commission accepted (c).
Question 27Hard
A beam with a central span L between supports and two equal overhangs L₁ carries a UDL w throughout. The maximum positive bending moment equals the maximum negative bending moment. The ratio L₁/L is:
All three statements describe the shear centre correctly. (This question was cancelled in the revised key.)
Question 30Easy
Which of the following statements is true? A: A roller is provided at one end of a bridge truss to allow thermal expansion. B: A roller provides freedom of deformation in the horizontal plane in case of thermal expansion.
A roller gives only a reaction normal to its bearing surface and lets the end move horizontally, so temperature changes do not cause stresses. Both statements are true.