Beam Analysis Problem For this problem: Force Units = kip Length Units = in E =

Question

Beam Analysis Problem For this problem: Force Units = kip Length Units = in E = 29000 ksi for all truss members I = 250 in4 for all truss members Determine the following for this structure: Determine the stiffness matrix for element 2, k?. Which D.O.F.'s for the structure arc restrained? How large will the system stiffness matrix be once boundary conditions arc applied? Determine the reduced joint load vector for the entire structure. Q_ir Determine the fixed-end force vector for element 2. Q_c.

Explanation / Answer

Stiffness matrix = EI/L3 * matrix of 12 6L -12 6L

                                                          6L 4L2 -6L 2L2  

-12 -6L 12 -6L

6L 2L2 -6L 4L2

=278,846.15 matrix of         12 156 -12 156

                                              156 2704 -156 1352

                                               -12 -156 12 -156

                                                156 1352 -156 2704

c)load vector

matrix of ( p1 p2 p3 p4 p5 p6 p7 p8) = matrix of ( -Pb/L -Pab2/L2 -Pb/L+WL/2 -(wL2/12-Pba2/L2) -(wL/2 + wL/3)   -(WL3/27 - WL2/12) Wl/3+2P WL2/12) = matrix of (-12.86 -12.9 -532.8 -8.4*103 540 -821 60 100)

d)Force vector (F1 F2 F3 F4) = Stiffness matrix k * displacement matrix

                                                         

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