civil engineering homework. Accuracy will be tested.

80' 80' 80' 20' 20'40'

A B C D E F G

40' 40'

Problem 1 (2%) Draw, to a reasonable scale, the influence line for the reaction at A for the beam shown above. Label all critical values on the I.L. Problem 2 (2%) Draw, to a reasonable scale, the influence line for the reaction at E for the beam shown above. Label all critical values on the I.L. Problem 3 (2%) Draw, to a reasonable scale, the influence line for the moment at B for the beam shown above. Label all critical values on the I.L. Problem 4 (2%) Draw, to a reasonable scale, the influence line for the moment at F for the beam shown above. Label all critical values on the I.L. Problem 5 (2%) Draw, to a reasonable scale, the influence line for the shear at F for the beam shown above. Label all critical values on the I.L. Problem 6 (2%) Draw, to a reasonable scale, the influence line for the shear at C for the beam shown above. Label all critical values on the I.L. Problem 7 (3%) Determine, using an influence line, the maximum downward reaction (љ) at A due to a 2 kips/ft live load for the beam shown above. Problem 8 (5%) Determine, using an influence line, the maximum shear at F for the beam shown above due to the truck shown below. The truck can travel left-to-right (as shown) or right-to-left.

14' 14'

24k 24k 6k

Problem 9 (15%) Determine the vertical deflection magnitude and direction at point C under the concentrated load for the structure shown below. Use the conjugate-beam method. E = 29,000 ksi, I = 1000 in4

4EI EI

10'

HINGE

10' 20' 30'

60�kips

A B C D

Problem 10 (15%) Determine the rotation magnitude and directions at point A due to the uniformly distributed load, w. Use the method of Virtual Work.

EI L

A B w

Problem 11 (10%) Determine the moment magnitude and direction at point A due to the uniformly distributed load, w. Use the Force Method.

EI

L

A

B w

Fx

Fy

AE/2

2.31AE

kspring 1

2

3

4

L

30°�

y

x

Problem 12 (6%) Assemble the transformation matrix for each of the 3 elements. Clearly label all DOFs on the drawing above. Problem 13 (6%) Write the local element stiffness matrix for each element. Clearly label all DOFs for each matrix. Problem 15 (12%) Compute the global element stiffness matrix for each element. Clearly label all DOFs for each matrix. Problem 15 (5%) Write the structure global stiffness matrix. Clearly label all DOFs for the structure global stiffness matrix. Problem 16 (3%) Write out the specific matrix equation needed to determine joint 1 displacements. Problem 17 (5%) Write out the specific matrix equation needed to determine reactions at joints 2, 3, and 4. Problem 18 (3%) Write out the specific matrix equation needed to determine the force in the spring.