15 questions. Tap an option to check it instantly, then read the solution.
Practice SSC JE and other civil engineering exam questions on slope and deflection of beams: the differential equation of the elastic curve, double integration and Macaulay's method, boundary and symmetry conditions, Mohr's moment-area theorems, standard slope and deflection formulas for cantilevers and simply supported beams, superposition and compatibility problems, strain energy and Castigliano's theorem. Tap an option to check it, then open the full explanation for each question.
Question 1Hard
An overhanging beam ABC is pinned at A and on a roller at B (span AB = 6 m, overhang BC = 3 m) and carries a 10 kN downward point load at C. Macaulay's method gives EIy = −(5/6)x³ + C₁x + (5/2)[x − 6]³, with x measured from A (kN, m). Find the slope at A if EI = 10 × 10¹³ N·mm².
y = 0 at B (x = 6): −(5/6)(216) + 6C₁ = 0 ⇒ C₁ = 30 kN·m². θA = C₁/EI = 30 × 10⁹ / (10 × 10¹³) = 0.0003 rad. (The original question printed C₁ as 0 and was cancelled.)
Question 2Easy
The integration constant C₁ used in Macaulay's method of analysis is obtained by applying ______ to the first integral (slope equation) of the differential equation of the elastic curve.
First integration gives the slope equation with C₁, which is fixed by a known slope (e.g. dy/dx = 0 at a fixed end or at mid-span of a symmetric beam).
Question 3Easy
A cantilever ABC, fixed at A, carries downward point loads of 20 kN at B (2 m from A) and 10 kN at the free end C (1 m beyond B). EI is constant. The slope at the fixed end A is:
Macaulay's method uses bracket (step) functions ⟨x − a⟩ that switch on at load points — these are singularity functions.
Question 5Medium
A cantilever AB of length l is fixed at A and carries a point load W at the free end B. Using the double integration method with x measured from the fixed end A, the slope dy/dx at any section is (EI = flexural rigidity):
EI y'' = −W(l − x). Integrate: EI y' = −W(lx − x²/2) + C; y' = 0 at x = 0 ⇒ C = 0. So dy/dx = −W(2lx − x²)/(2EI).
Question 6Easy
For a cantilever AB (fixed at A) of length L carrying a point load P at the free end, the slope equation from the double integration method is EI dy/dx = −P(Lx − x²/2), with x measured from the fixed end. The maximum deflection is:
EIy = −P(Lx²/2 − x³/6) + C; y = 0 at x = 0 ⇒ C = 0. At x = L: EIy = −P(L³/2 − L³/6) = −PL³/3.
Question 7Medium
A cantilever AB of length 5 m (fixed at A) carries a uniformly varying load whose intensity is 20 kN/m at the fixed end A and zero at the free end B. EI is constant. The slope at the free end is:
The slope at the fixed support of a cantilever of length L and flexural rigidity EI, carrying a point load P at mid-span and another point load P at the free end, is:
What is the deflection at the free end of a cantilever of length L carrying a point load P at its free end? (E = Young's modulus, I = moment of inertia)
The moment distribution (Hardy Cross) method finds support/joint moments in indeterminate structures, not deflections.
Question 14Hard
A cantilever of span l is fixed at one end, and its other end rests freely on the middle of a simply supported cross-beam of the same span and section. If the cantilever carries a UDL of w per unit length, the reaction at its free end offered by the cross-beam is:
A cantilever of span L carries a uniformly distributed load of w per unit length. The maximum deflection in the beam is (E = modulus of elasticity, I = moment of inertia):