When an initially straight beam sags under transverse loading, the ends contract because the neutral surface of zero strain neither extends nor contracts. The length of the deflected neutral surface is the same as the original beam length l. Consider a segment of the initially straight beam Δs. After bending, the x-direction component is shorter than Δs, namely, Δx. The contraction is Δs −Δx , and these summed for the entire beam gives the end contraction λ. Show that λ =
Answer to relevant QuestionsUsing the results of Prob. 4–9, determine the end contraction of the uniformly loaded cantilever beam of appendix Table A–9–3.A rectangular steel bar supports the two overhanging loads shown in the figure. Using superposition, find the deflection at the ends and at the center.The structure of a diesel-electric locomotive is essentially a composite beam supporting a deck. Above the deck are mounted the diesel prime mover, generator or alternator, radiators, switch gear, and auxiliaries. Beneath ...The rectangular member OAB, shown in the figure, is held horizontal by the round hooked bar AC. The modulus of elasticity of both parts is 10 Mpsi. Use superposition to find the deflection at B due to a force F = 80 lbf.Find ...Solve Prob. 4–15 using singularity functions. Since the beam is symmetric, only write the equation for half the beam and use the slope at the beam center as a boundary condition. Use statics to determine the reactions.
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