CE 272A/CE 222ASSIGNMENT # 10

Use the Matrix Displacement Method to solve the following problems,while taking global axes, x′ and y′, directed respectively as horizontallyto the right and vertically upwards.

1. Find the displacements of point 2 and the forces in the bars of the truss shownin Fig. 1. Both bars have the same AE values. [Ans. u2 = −16WL/3AE, F23= 5W/3]

2. Calculate the displacements of point B of the truss shown in Fig. 2. The cross-sectional area of BC and BE is

√2A and of all other members is A. Young’s

modulus is E for all bars. Determine the forces acting in the bars. [Ans. vB =WL/AE, FBC = 3W/2

√2]

3. Each of the five bars of the truss shown in Fig. 3 has a cross-sectional area of2000 mm2, with E = 200 GPa. Find all unknown joint displacements in the trussand axial forces in the bars. [Ans. u2 = 0.150 mm, v3 = −0.475 mm, F23 =−40 kN]

4. Determine the nodal displacements of the truss shown in Fig. 4. Hence, calculatethe axial forces in bars 1–3 and 3–5. The axial rigidity is AE for bars 3–4 and4–5, and 2AE for the other bars, with AE = 500 MN.

5. Repeat Problem # 4 by using SAP 2000 (Educational Version).