4. A bar assembly with 3 elements is loaded with horizontal forces 400 lbs at node 2 and 400 lbs at node 3 as shown in the figure. Node 1 represents the contact point between element 1 (as well as element 2) and a fixed support.
The bar assembly is made of a homogeneous material with a Young's modulus E= 20,000 psi. Element 1 and 2 has a length of 10 inches and a cross-sectional area of 1 in², element 3 has a length of 3 inches, and a cross-sectional area of 6 in². Use one-dimensional finite element method to solve and answer the following questions.
Fixed
support
E= 20,000 lb/in²
$$A_1 = 1 \text{ in}^2$$
$$A_3 = 6 \text{ in}^2$$
1
400 lb
2
3
400 lb
$$A_2 = 1 \text{ in}^2$$
10 in
3 in
(3%)
(a) What are the displacement variables you would define each of the 3 nodes?
(3%)
(b) What's the boundary condition?
(4%)
(c)What are the external loads?