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ENGR5004 / Week 7
Tutorial 2 Problem 2Exercise sheetCurrent spec2:125 min

ENGR5004 Statics Tutorial Sheet 2, Problem 2 official answers

Consider the loaded beam shown below, subject to a parabolic distributed load, constrained by a fixed support at its left end, and a roller at its right end.

Beam AB, L = 3 m, fixed at A (left), roller at B (right), parabolic load w = w0 (x/L)^2 rising from zero at A to w0 at B.
Beam AB, L = 3 m, fixed at A (left), roller at B (right), parabolic load w = w0 (x/L)^2 rising from zero at A to w0 at B.
Formulas you may need
  • Distributed load resultant P=∫w dxP = \int w\,dx and its position xPx_P (on the formula sheet)
  • Load-shear-moment relations: dVdx=−w\dfrac{dV}{dx} = -w, dMdx=V\dfrac{dM}{dx} = V (on the formula sheet)
  • Elastic curve: EId2ydx2=M(x)EI\dfrac{d^2y}{dx^2} = M(x), θ=dydx\theta = \dfrac{dy}{dx} (learn this; on the 2025 sheet but not the 2026 one)
  1. (a)
    State if this structure is statically determinate or indeterminate and justify your answer;
  2. (b)
    knowing that the distributed load per unit length at the right end (end B) is w0=15w_0 = 15 kN/m, and the beam length is L=3L = 3 m, determine the reactions at the fixed support and the roller.