Bedford

Problem 6.1 In Active Example 6.1, suppose that in addition to the 2-kN downward force acting at point D, a 2-kN downward force acts at point C. Draw a sketch of the truss showing the new loading. Determine the axial forces in members AB and AC of the truss.

A 3m C 3m B D 5m 5m 2 kN

Solution: The new sketch, a free-body diagram of the entire truss
and a free-body diagram of the joint at Aare shown. The angle ˛ between CD and BD is ˛ D tan
1

6/10 D 31.0°

Using the entire truss, the equilibrium equations are Fx : Ax C B D 0 Fy : Ay MA : 2 kN 2 kN D 0 2 kN 10 m

2 kN 5 m

CB 6 m D0 Solving yields Ax D 5 kN, Ay D 4 kN, B D 5 kN

Using the free-body diagram of joint A, the equilibrium equations are: Fx : Ax C TAC cos ˛ D 0 Fy : Ay TAB TAC sin ˛ D 0

Solving yieldsTAB D 1 kN, TAC D 5.83 kN Because both values are positive, we know that both are in tension AB : 1 kN (T), AC : 5.83 kN (T)

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Problem 6.2 Determine the axial forces in the members of the truss and indicate whether they are in tension (T) or compression (C).

20 A

800 N

0.4 m C B 0.7 m 0.7 m

Solution: We start at joint A
Fx : 7 7 p FAB C p FAC 65 65 4 p FAB 65 4 p FAC 65 800 N sin 20° D 0

Next we move to joint C Fx : 7 p FAC 65 FBC D 0 ) FBC D 521 N

FAC
800 N cos 20° D 0 600 N

Fy :7 4 C

Solving we have

FAB D

915 N, FAC D

20° 800 N FCB

Cy A 4 7 FAB 4 7 FAC
In summary we have FAB D 915 N C , FAC D 600 N C , FBC D 521 N T

Problem 6.3 Member AB of the truss is subjected to a 1000-lb tensile force. Determine the weight W and the axial force in member AC.
60 in

A

W B 60 in C 60 in 2
1 p FAC D 0 2

Solution: Using joint A
Fx : 2 p 1000 lb 5 1 p1000 lb 5 FAC D

A

1 1000 lb 1 1 FAC W

Fy :

1 p FAC 2

WD0

Solving we have

1265 lb, W D 447 lb

In summary we have W D 447 lb, FAC D 1265 lb C

c 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means,without permission in writing from the publisher.

387

Problem 6.4 Determine the axial forces in members BC and CD of the truss.

600 lb

E

3 ft C D

3 ft

A 3 ft

B 3 ft

Solution: The free-body diagrams for joints E, D, and C are shown. The angle ˛ is
˛ D tan Using Joint E, we have Fx : Fy : 600 lb TCE cos ˛ TCE sin ˛ D 0 TDE D 0
1

3/4 D 36.9°

Using Joint D, we have Fx: TCD TBD sin ˛ D 0 TBD cos ˛ D 0

Fy : TDE

Finally, using Joint C, we have Fx : TCD C TCD sin ˛ Fy : TCE cos ˛ TAC sin ˛ D 0 TBC D 0

TAC cos ˛

Solving these six equations yields TCE D TCD D 1000 lb, TDE D 800 lb 600 lb, TAC D 2000 lb

TBC D 800 lb, TBD D 1000 lb A positive value means tension and a negative value means compression Thus BC : 800 lb (T), CD : 600 lb (C)

388

c2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Problem 6.5 Each suspended weight has mass m D 20 kg. Determine the axial forces in the members of the truss andindicate whether they are in tension (T) or compression (C).

A

0.4 m C D

B

m

m

0.16 m 0.16 m

0.32 m

Solution: Assume all bars are in tension. Start with joint D
5 Fy : p TAD 61 Fx : Solving: 6 p TAD 61 196.2 N D 0

Finally work with joint A Fy : 5 p TAB C TAC 29 423 N 5 p TAD D 0 61

TCD D 0

) TAB D

T
235 N

TAD D 306 N, TCD D

A 2 6 5 2 5

TAD 5 6 D TCD TAB...