Consider the structure AHB shown below. Both parts (AH and BH) have the same cro

Question

Consider the structure AHB shown below. Both parts (AH and BH) have the same
cross section and elastic modulus, and therefore the same EI.
a) First, derive the equation of the elastic curve for a cantilever beam AH alone with a
concentrated load, P, at the end (shown on the left). What is the vertical deflection at H?
Give your answer in terms of P, L, and EI.
b) For the combined structure, AHB, what is the vertical deflection at H if P = 30 kips, L = 3
ft, a = 1.8 ft, E = 10,000 ksi, and I = 100 in4? Use the method of superposition.

Explanation / Answer

a) at any distance x from H
Moment = M = -Px
EI y'' = -Px
EI y' = -Px^2/2 + c
at x = L y' = 0
c = PL^2/2

EI y = PL2x/2 - Px3/6 + k

at x= L y = 0

k = - PL3/3

so EI y = PL2x/2 - Px3/6 - PL3/3

at x=0

EI y = - PL3/3

y = - PL3/3EI

at H deflection is - PL3/3EI

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