CE595- Finite Elements in Elasticity
EXAM No. 2
Consider the concrete dam structure shown below. Assume that the concrete will have a nominal
compressive strength of 3500 psi. Develop a finite element model for the structure. Analyze the
model for two loa
CE 595 HW5 Soln
LYC
1/4
1. Shape function matrix w.r.t. the generalized coordinates:
Ns ( x , y ) :=
1 x y 0 0 0 0 0 0 1 x y
Answer
2. Shape function matrix w.r.t nodal displacement: Interpolation approach
u1 v1 u2 u := v2 u3 v3
a1 a2 a3 a := a4 a5 a6
CE 595 Finite Elements in Elasticity Exam No. 1 Problem No. 1
A. Varma Due: March 23, 2009 (Worth 30 points)
A solid column with varying cross-sectional area (A=Ao ey/L) as shown in Figure 1 is subjected to uniform loading at the top. This loading produce
CE595- Finite Elements in Elasticity EXAM No. 2 Assigned: April 10, 2009 Due: April 24, 2009 Consider the concrete dam structure shown below. Assume that the concrete will have a nominal compressive strength of 3500 psi. Develop a finite element model for
Geometric Stiffness Matrix for the Truss Element
Geometric Stiffness Matrix for the Beam Element
Example using Beam Element
W27 x 84
50 kips
100 kips
10 kips B
Ab = 24.8 in2
Ib = 2850 in4
D
50 kips
F
E= 29000 ksi
288 in.
W10 x 45
Ac = 13.3 in2
Ic = 248 in
CE 595: Finite Elements in Elasticity
HW#1 Solutions
Problem #1
Given: A cantilevered beam has a length L, constant cross-sectional area A, constant moment of inertia
1 x
I z , and a variable Youngs modulus E (x ) = Eo ( + L ). It is loaded by a verticall
CE 595: Finite Elements in Elasticity
HW#1 Problem
Problem #1
Given: A cantilevered beam has a length L, constant cross-sectional area A, constant moment of inertia
1 x
I z , and a variable Youngs modulus E (x )= Eo ( + L ). It is loaded by a vertically u
CE 595 Finite Elements in Elasticity
Homework No. 2
For the beam-column problem shown below, use variational calculus to determine the governing
differential equation, and the associated natural and forced boundary conditions at the ends.
Use the given en
CE595:
Homework No. 6
Given: Cantilevered beam with dimensions shown; rigidly fixed at x = 0; applied
traction at x = 18. E = 27,000 ksi; = 0.25. Additional loading due to self-weight of steel
= 0.003 k/in3.
Required: Using CST plane stress elements, find
CE 595 Finite Elements in Elasticity
A. Varma
Exam No. 1
Problem No. 1
(Worth 30 points)
A solid column with varying cross-sectional area (A=Ao ey/L) as shown in Figure 1 is
subjected to uniform loading at the top. This loading produces stress o at the to