Spring 2014 CE 3303

The beam shown is fixed at A and D and has internal hinges at B and C. (External Equilibrium)

1) Draw the free body diagram of each beam: AB, BC, and CD. (9 points)

2) Determine the Horizontal Reaction at A. (3 points)

3) Determine the Vertical Reaction at A. (3 points)

4) Determine the Moment Reaction at A. (3 points)

A

C D

B 178 kip ft

184 kip ft

172 kip ft

196 kip ft

A

C D

B 34 kip

52 kip

22 kip

19 kip

A

C D

B 16 kip

8 kip

0

8 kip

B

C D

A

B C

A

3 kip

B C D

6 kip

6 ft 4 ft 16 ft 4 ft 6 ft

2 kip/ft

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Spring 2014 CE 3303

The planer frame shown is fixed at its support. All members are rigidly/fixed connected to each other. Use our sign convention for internal forces with compression on the left side of the column caused by a positive internal moment. (Internal Equilibrium)

5) Determine the Normal Force at Section A-A. (4 points)

6) Determine the Shear Force at Section A-A. (4 points)

7) Determine the Moment at Section A-A. (4 points)

A

C D

B 96 kip ft

320 kip ft

256 kip ft

192 kip ft

A

C D

B 20 kip

12 kip

4 kip

16 kip

A

C D

B 32 kip (C)

52 kip (C)

28 kip (C)

36 kip (C)

A

2 kip/ft

4 kip

A

16 ft

10 ft

6 ft

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Spring 2014 CE 3303

The following assembly has the loads applied to it as shown. (Axial/Normal Force Diagram)

8) Draw the Axial/Normal Force Diagram. (8 points)

(T) N ______

(C)

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Spring 2014 CE 3303

The following bar has the torque loads applied to it as shown. (Torsion Force Diagram)

9) Draw the Torsion Force Diagram. (8 points)

+ T ______

-

5 kNm

3 kNm

B C A

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Spring 2014 CE 3303

For the beam and loading shown it is determined that RAy = 6 kip and RBy = 10 kip. (Shear and Moment Diagram)

10) Complete the free-body diagram showing all forces and moments for the beam segment from A to C. Determine the internal forces (magnitude and sign) in the beam at location C, 7 ft from the left end. (10 points)

Nc@ x=7' = _________ Vc@ x=7' = _________ Mc@ x=7' = _________

11) Draw the shear and moment diagrams, showing all significant values of shear and moment. (20 points) 12) Determine the maximum shear V (magnitude and sign) and the maximum bending moment M (magnitude and sign) in the beam. (6 points) Vmax = _________ Mmax = _________

5 ft 3 ft 3 ft 2 ft

B A

2 kip/ft 5 kipft

+

-

+

-

2 ft C

10 kip 3

4

V ______

M ______

x = 7 ft

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Spring 2014 CE 3303

5.0 kip3.0 kipft10.0 kip ft

10.0 ft4.0 ft 4.0 ft

21.0 kip 14.0 kip

x1

x2

x3

The beam in the figure is simply supported and loaded as shown. For both equations, x1 and x2 should be measured from the LEFT end of the beam and x3 should be measured from the RIGHT end of the beam.

13) Sketch the free-body diagram and write an equation for the moment in the section of the beam based on x2: 4.0 14.0ft x ft (9 points) M2 = ____________________ 14) Sketch the free-body diagram and write an equation for the moment in the section of the beam based on x3: 0.0 4.0ft x ft (9 points) M3 = ____________________

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