F13Q1_1: COMPOSITE BAR UNDER DISTRIBUTED LOADING
The composite bar AB has length L and is fixed at A(x=0).
The bar has a constant cross-section and is composed of two steel plates, of modulus Es=2E0 sandwiching a copper core of modulus Ec=E0.
The steel plates and the copper core have equal width w and equal height h.
The bar is subjected to a distributed load per unit length of the bar fx(x)=p0(xL)13.
The given known quantities are:
L=2m
h=3cm
w=2cm
E0=100GPa
p0=1000kN/m
Helpful hint:
∫xndx=xn+1n+1+Constant
Obtain a symbolic expression for the axial force resultant, N(x), in terms of L, x and p0 (enter this as p_0):
N(x)=
Obtain the numerical value of the axial force resultant at A, N(x=0), in kN.
N(x=0)=
Obtain a symbolic expression for the elongation of bar AB, δAB, in terms of L, h, w, E0, and p0.
δAB=
Obtain the numerical value of the elongation of bar AB, δAB, in mm.
δAB=
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