An aluminum pipe (modulus of elasticity 10.1x10^6 psi) is fixed at one end and is subjected to a tensile load of 127.5 kips at the free end. The length and cross-sectional area of the pipe is given as 36.1 in and 9.11 in^2. Assume that the aluminum pipe has clockwise torques (100 lb-in) acting at the midpoint and free end of the pipe. (a) Derive the element stiffness matrix

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Problem 1.5.6P: The data in Table 1.5.3 were obtained from a tensile test of a metal specimen with a rectangular...
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An aluminum pipe (modulus of elasticity 10.1x10^6 psi) is fixed at one end and is subjected to a tensile load of 127.5 kips at the free end. The length and cross-sectional area of the pipe is given as 36.1 in and 9.11 in^2. Assume that the aluminum pipe has clockwise torques (100 lb-in) acting at the midpoint and free end of the pipe. (a) Derive the element stiffness matrix 

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Element stiffness matrix for a cantilever beam subjected to both axial load and moment will be the combination of the axial stiffness matrix(Kaxial) and the (Kbending).

KaxialAEL0

Kbending =2EILLEI

Where A is the cross-sectional area of the beam = 9.11 in2

E is the modulus of elasticity, E = 10.1×106 psi

L is the length of the beam = 36.1 in

I is the moment of inertia of the beam cross section.

If Area, A =π4d2 =9.11

d = (9.11×4π)=3.4 in

So moment of inertia, I = π64×d4

I =π64×3.44=6.56 in4

Axial load, P = 127.5 kips

Torque at mid point and free end is same and its value is, M = 100 lb-in

 

 

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