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1 Department of Civil and Environment Engineering CGN 4980/CGN 6939 FE/Graduate Seminar Review Examples Fall 2005.

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Presentation on theme: "1 Department of Civil and Environment Engineering CGN 4980/CGN 6939 FE/Graduate Seminar Review Examples Fall 2005."— Presentation transcript:

1 1 Department of Civil and Environment Engineering CGN 4980/CGN 6939 FE/Graduate Seminar Review Examples Fall 2005

2 2 Determine the force in each member of the truss and state if the members are in tension or compression. Solution:

3 3

4 4

5 5 F DC F DE

6 6 F AB

7 7 F FE F FB

8 8 F FE F FB

9 9 F BE F BA F BC

10 10 F EC F EF F ED

11 11 F CD F CB

12 12 The rod has a weight W and rests against the floor and wal for which the coefficients of static friction are  A and  B, respectively. Determine the smallest value of  for which the rod will not move. Given: Find: Solution:

13 13 FAFA NANA NBNB W L sin  FAFA FBFB Impending Motion at All Points

14 14 FAFA NANA NBNB W L sin  FAFA FBFB Equilibrium Eqs.

15 15 FAFA NANA NBNB W L sin  FAFA FBFB slipping must occur at A & B

16 16 The three bars have a weight of W A = 20 lb, W B = 40 lb and W C = 60 lb, respectively. If the coefficients of static friction at the surfaces are as shown, determine the smallest horizontal force P needed to move block A. Given: Find: Solution:

17 17 N AD F AD T ABC W ABC

18 18 N AD F AD AB W AB F BC C +Tsin  N CB =W C +Tsin  N CB F CB T CWCCWC If blocks A & B move first

19 19 N AD F AD AB W AB F BC C +Tsin  N CB =W C +Tsin  N CB F CB T CWCCWC If blocks A & B move first

20 20 F AB T T If blocks A move first N AB N AD F AD AWAAWA F AB N AB CB W CB Therefore block A moves first

21 21 Given:rod,  Find:x Solution: Determine the distance x to the center of mass of the homogeneous rod bent into the shape shown. If the rod has a mass per unit length of 0.5 kg/m, determine the reactions at the fixed support O.

22 22

23 23

24 24

25 25 Locate the centroid of the quarter circle shown in the figure.

26 26

27 27

28 28

29 29

30 30 Find the Centroid

31 31 1 2 3

32 32 1 2 3

33 33 Each of the three members of the frame has a mass per unit length of 6 kg/m Locate the position (x, y) of the center of gravity. Neglect the size of the pins at the joints and the thickness of the members. Also, locate the reactions at the pin A and roller E. Solution:

34 34 1 2 3

35 35 1 2 3

36 36 1 2 3

37 37 Determine the moment of inertia I y for the slender rod. The rod’s density  and cross-sectional area A are constant. Express the results in terms of the rod’s total mass m.

38 38


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