Mechanical Engineering Risa 2D finite Element Analysis

CIVE 5522 STRUCTURAL ANALYSIS 2

ASSIGNMENT NO. 5

Due: Tuesday, Feb. 27, 2018 (beginning of class)

Read Chapter 17 (Leet et al.)

1. Use the direct stiffness method to determine the displacement components at node 𝑎

(specify directions by using arrows) and the member forces (specify T or C) for the plane truss shown below. Verify force equilibrium at node 𝑎. 𝐴!" = 1.2 in!,𝐴!" = 1.0 in!,𝐴!" = 3.6 in! and 𝐸 = 29,000 ksi

2. The figure below shows a two-member plane truss supported by a linearly elastic spring.

Using the direct stiffness method, determine the nodal displacements (specify direction by using arrows) and the forces in each member (specify T or C). Let 𝐴 = 300 mm2 and 𝐸 = 80 GPa for all truss elements. The linear spring has stiffness constant 𝑘 = 50 N/mm.

1

2

3

4

3. If the end displacements in the global coordinate system for member 5 of the truss

shown below are given as: ∆!! ∆!! ∆!! ∆!!

= −0.064655 −0.19398

0 0

in

a) Calculate the axial force in member 5 (specify if the member is in T or C). b) Calculate the end forces for member 5 in the global coordinate system using

matrix equations. Is the member in equilibrium under these forces?

4. For the plane truss shown below, use the direct stiffness method and symmetry to determine the displacements of the joints (specify direction by using arrows), and the force in member 5 (specify T or C).

x

y