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Problem 3 (7pts) a) See below as the system consisting of a spring and two rods. You can assume that the two rods are connected by a rigid link. Calculate the elongations of the rods and the spring using energy method. Rigid lin E, A, L k-4EA/L E, 2A, L b) See below as a beam that is supported by an array of springs. Solve for the approximate solution of the vertical displacement (v) as a function of z, using the energy principle. L/2 E, I Spring constant per length k

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Answer #1

a) here the stiffness of each bar is calculated and we can find the total stiffness

Stiffness K= load(F)/deflection(d)

K=F/d , displacement of spring(d) = F/K=FL/(4EA)

Elongation of rods can be found in similar manner

Here stiffness of each bar is calculated and total stiffness is calculated

K1for rod1 = EA/L

K2 for rod2 = 2EA/L

Keq=K1+K2= 3EA/L

The elongation of rods = F/Keq

d= FL/3EA

b) here we can generate an equivalent spring Keq=17k

Taking momentum equation

Reaction at pin joints are Ra and Rb taking moment about a then F=Rb + Kd/2

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