Mechanical Engineering Risa 2D finite Element Analysis

CIVE 5522 STRUCTURAL ANALYSIS 2

ASSIGNMENT NO. 6

Due: Tuesday, March 13, 2018 (beginning of class)

Read Chapter 18 (Leet et al.) and class notes

1. Use the direct stiffness method to determine the rotations at the supports and the

shear force and bending moment diagrams for the continuous beam shown below. 𝐸𝐼 is constant.

2. For the beam shown below, use the direct stiffness method to determine all the joint

displacements (including rotation and vertical displacement at joint 3), the member end forces, and the reactions. The forces in each member (with correct directions) must be presented on a free-body diagram of the member.

3. Using the direct stiffness method analyze the beam shown below if, in addition to

the loading given, the support at 𝑏 settles 0.03 m downward. Determine the displacements/rotations at the joints, the forces in each element, and the reactions. The forces in each element (with correct directions) must be presented on a free- body diagram of the element. Let 𝐸𝐼 = 400 MN-m2.

4. Use the direct stiffness method and symmetry to find the displacements and rotations at the nodes/joints, the vertical displacement at the midspan, the forces in each element/member, and the reactions. The forces in each element (with correct directions) must be presented on a free-body diagram of the element. Let I = 4.8 x 109 mm4 and E = 30 GPa.

5. Use the direct stiffness method to analyze the rigid frame shown below. In this problem you will account for axial deformations. a) Identify the degrees of freedom and the restrained coordinates/displacements as

well as establish the global coordinate axes. b) Determine the fixed end force vector for each member in local coordinates {𝑓!},

and in global coordinates {𝑓!}!. c) Determine the stiffness matrix for each member in global coordinates [𝑘]. For

simplicity, you can compute only those coefficients related to the dof’s. d) Determine the structure stiffness matrix [𝐾] (reduced stiffness matrix), assemble

the nodal force vector {𝐹} and solve for the unknown joint displacements. e) Compute the member local end forces in each element/member. The forces with

correct directions must be presented on a free-body diagram of the element.