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Material Type: Assignment; Class: ELEM STRUC I; Subject: Civil and Environmental Engineering; University: University of Washington - Seattle; Term: Autumn 2007;
Typology: Assignments
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(Due in-class, Oct. 19th) You can work in groups of 2-4 to complete this assignment. Turn in only one assignment per group. Write the names of all members of the group on this sheet.
Names: 1.
In all problems, consider a truss member a cross-sectional area, A = 10.0 in^2 , a modulus of elasticity, E=29 x 10^3 ksi, and a yield stress of 50 ksi (with no strain hardening). The nodal coordinates of the member are as follows: XN = 10 in. YN = 0. in. XF = 10 in. YF = 150 in.
Problem 1. Compute the element stiffness matrix for this member.
L = AE/L =
cos θx =
sin θx = cos θy
Problem 2. Consider the following set of end displacements. DNX = 0 in. DNY = 0 in. DFX = 1.5 in. DFY = 0 in. a) Calculate the element nodal forces and axial force using the element stiffness matrix computed in Problem 1.
b) Considering the actual deformed geometry , the actual change in length and the actual stress-strain relationship, calculate the element nodal forces and axial force for the same set of joint displacements.
ε =
σ =
P =
new θ =
QNx = QNy = QFx = QFy =
c) Compare the results of your calculations for parts a and b. How are they the same or different?