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ENGR5004 / Week 3
Old spec Statics Session 6 Review ProblemTutorialOld spec ENGR216Third10 min

ENGR216 (old spec) Statics session 6 worked example 2 (Appendix review problem, slides 17-23) official answers

A simply supported beam AB of length LL (pin at A, roller at B) carries a uniform distributed load WW (N/m) over its whole length and a concentrated load PP (N) at midspan. Using superposition (uniform load alone plus concentrated load alone), determine the shear force and bending moment along the beam and sketch both diagrams.

Simply supported beam of length L (pin at A on the left, roller at B on the right) with a uniform load W along the whole span and a concentrated load P at midspan; x measured from A.
Simply supported beam of length L (pin at A on the left, roller at B on the right) with a uniform load W along the whole span and a concentrated load P at midspan; x measured from A.
Formulas you may need
  • Positive shear and positive bending sign convention (pictures); dVdx=−w\dfrac{dV}{dx} = -w, dMdx=V\dfrac{dM}{dx} = V (on the formula sheet)
  • Equilibrium ∑Fy=0\sum F_y = 0, ∑M=0\sum M = 0 for the reactions; method of sections (learn this)
  • Superposition of load cases for a linear structure (learn this)