SE 130A_HW6_WI13

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University of California, San Diego Department of Structural Engineering

Winter 2013 Instructor: Chia-Ming Uang

SE 130A – Structural Analysis I

Homework Set No. 6 (Due Date: March 1, 2013 at 5:00pm)

Note: 1) Textbook refers to Fundamentals of Structural Analysis, Fourth Edition, by Leet, Uang, and Gilbert.

2) An educational version of the structural analysis software called RISA-2D, as well as a tutorial, is

available from TED. It will be required for Problems 2 and 4, but you can also use this simple softwareto verify answers to all problems.

(1) Do P.12.4 in the textbook but with a concentrated moment of 24 kN-m in place of the vertical 24 kN load

at mid-span of AB.

(a) Draw the shear and moment diagrams.

(b) Compute all support reactions.

(c) Sketch the deflected shape.

(d) What is the change in moment at A if the moment of inertia of member AB is doubled?

(e) What is the effect of using a softer material, say with ½ E , on the moment at A and the rotation at B?

(2) Analyze the structure shown in Figure 1 by the slope-deflection method and draw the moment diagram.

E is constant and the moment of inertia is shown in the figure. Check the moment diagram by RISA-2D.

15 kips

3 kips/ft

8 ft

6 ft 5 ft 6 ft5 ft

A

CB

D

I

I

2 I

I

Figure 1

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(3) Determine the rotation, in radians, at B as well as the reactions at A and D of the frame shown in

Figure 2. Using E = 29,000 ksi and I = 100 in4

for all members, consider the following two cases:

(a) In addition to the applied loading shown, support D is constructed 3 in. too low.

(b) In addition to the applied loading shown, support A settles by 3 in.

8 ft

A

B

8 ft

10 kips

20 kips20 kips

9 ft 4 ft 9 ft

C

D

(4) Consider the continuous beam shown in Figure 3. EI is constant, except the 5 ft segment supported at

Point C is rigid (i.e. EI →∞). A concentrated moment MO is applied at C. Solve the problem by the slope-

deflection method. Draw the moment diagram and deflected shape.

[ HINT: Translation of member AB is related to the rotation at C ]

12 ft3 ft

M 0

A B C D E

2 ft12 ft

Figure 3

Figure 2

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(5) Use the slope-deflection method to analyze the structure shown in Figure 4. Use E = 29,000 kips/in2,

I 1 = 180 in4, and I 2 = 240 in

4for the members as shown.

(a) Construct the moment diagram.


(c) Draw the deflected shape.

(d) Compute the horizontal deflection of Joint B and verify your answer by the computer

software RISA-2D.

12 kips/ft

9 ft

15 kips/ft

A

B C

D

I 1 I 2

I 2

9 ft

12 ft

Figure 4

(6) Use the slope-deflection method to analyze the structure shown in Figure 5, with k s =1450 kips/in,

E =29,000 ksi, and I = 500 in4.

(a) Draw the shear and moment diagrams.


(c) Sketch the deflected shape.

( HINT: Treat AC as one member )

Figure 5

150 kips

10 ft 10 ft 10 ft

k s

20 kip/ft

A B

C

D

E

SE 130A_HW6_WI13

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