Question

STA401M Assessment 1 APR 2022 Question 1 [30 marks] Consider the round bar assemblage depicted in Figure 1. The diameter of the bars is 50 mm and the modulus of elasticity is E = 210 GPa. Determine the nodal displacements, the forces in each element, and the reactions at element 1. Use the direct stiffness method 35 KN 25 KN 1 ? ? ? 3 0.8m 0.8m 0.8m X Figure 1: Three Bar Assemblage Question 2 [21 marks] Consider the spring assemblage depicted in Figure 2 with the spring constants $k_1$ = 400 N/mm and $k_2$ = 150 N/mm. Node 3 displaces an amount of $\delta$ = 15 mm as inindicated. Determine the displacement at node 2, the forces in each spring element, and the force $F_3$. $k_1$ 2 $k_2$ 3 $F_3$ X $\delta$ Figure 2: Spring Assemblage All the best!!!

          STA401M
Assessment 1
APR 2022
Question 1 [30 marks]
Consider the round bar assemblage depicted in Figure 1. The diameter of the bars is
50 mm and the modulus of elasticity is E = 210 GPa.
Determine the nodal displacements, the forces in each element, and the reactions at
element 1. Use the direct stiffness method
35 KN
25 KN
1
?
?
?
3
0.8m
0.8m
0.8m
X
Figure 1: Three Bar Assemblage
Question 2 [21 marks]
Consider the spring assemblage depicted in Figure 2 with the spring constants $k_1$ = 
400 N/mm and $k_2$ = 150 N/mm. Node 3 displaces an amount of $\delta$ = 15 mm as
inindicated.
Determine the displacement at node 2, the forces in each spring element, and the
force $F_3$.
$k_1$
2
$k_2$
3
$F_3$
X
$\delta$
Figure 2: Spring Assemblage
All the best!!!

STA401M
Assessment 1
APR 2022
Question 1 [30 marks]
Consider the round bar assemblage depicted in Figure 1. The diameter of the bars is
50 mm and the modulus of elasticity is E = 210 GPa.
Determine the nodal displacements, the forces in each element, and the reactions at
element 1. Use the direct stiffness method
35 KN
25 KN
1
?
?
?
3
0.8m
0.8m
0.8m
X
Figure 1: Three Bar Assemblage
Question 2 [21 marks]
Consider the spring assemblage depicted in Figure 2 with the spring constants k1 =
400 N/mm and k2 = 150 N/mm. Node 3 displaces an amount of δ = 15 mm as
inindicated.
Determine the displacement at node 2, the forces in each spring element, and the
force F3.
k1
2
k2
3
F3
X
δ
Figure 2: Spring Assemblage
All the best!!!

Added by Stephanie R.

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