Types of Structures & Loads

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1 Structure Analysis I Chapter 4 1 Types of Structures & Loads 1Chapter

2 Chapter 4 Internal lloading Developed in Structural Members

3 Internal loading at a specified Point In General The loading for coplanar structure will consist of a normal force N, shear force V, and bending moment M. These loading actually represent the resultants of the stress distribution acting over the member s cross-sectional are

4 Sign Convention +ve Sign

5 Procedure for analysis Support Reaction Free-Body Diagram Equation of Equilibrium

6 Eample 1 Determine the internal shear and moment acting in the cantilever beam shown in figure at sections passing through points C & D

7 V C M c F y = 0 = 15kN M C = 0 V = 50kN. m C M = 0 c 5(1) 5(2) 5(3) 20 = 0

8 kn V V F C D y = = = kn m M M M kn V D D C C (3) 5(2) 5(1) 0 20 = = =

9 Eample 2 Determine the internal shear and moment acting in section 1 in the beam as shown in figure 18kN RA = RB = 9kN 6kN V F y = 0 V = 0 y = 3kN M at section = 0 M + 6(1) 9(2) = M D = 12kN. m 0

10 Eample 3 Determine the internal shear and moment acting in the cantilever beam shown in figure at sections passing through points C

11 V Fy = 0 VC = 0 = 6k M c = 0 M D = 48 k. ft M c + 3(2) 9(6) = 0

12 Shear and Moment function Procedure for Analysis: 1- Support reaction 2- Shear & Moment Function Specify separate coordinate and associated origins, etending into regions of the beam between concentrated forces and/or couple moments or where there is a discontinuity of distributed loading. Section the beam at distance and from the free body diagram determine V from, M at section

13 Eample 4 Determine the internal shear and moment Function

14 Eample 5 Determine the internal shear and moment Function

15 w = = w w V F = + = ) ( V V F y = ) 30( 0 M M M S + = = + + =

16 Eample 6 Determine the internal shear and moment Function

17 0 <12 < V V F y = = + = < < ( ) S M M M V = + + = = M + =

18 12 < < 20 2 V M = F y M 60 S = = 0 = V M = ( 6) 2 = 0

19 Eample 7 Determine the internal shear and moment Function

20 w = w w (20) V F y = + = ) ( V y = ( ) (20) M M M S + = = =

21 Shear and Moment diagram for a Beam

22 0 ) ( ) ( 0 V V w V F = + + = ( ) O 0 ) ( ) ( 0 ) ( 0 ) ( ) ( 0 M M w M V M w V V V w V F y = + + = = = + + = ε ( ) ( ) 2 O ) ( ) ( ) ( w V M + = ε = = d w V w d dv for ) ( ) ( 0 d V M V dm d ) ( = = d V M V d ) (

23 Eample 1 Draw shear force and Bending moment Diagram S.F.D B.M.D

24 Eample 2 Draw shear force and Bending moment Diagram S.F.D B.M.D

25 Eample 4 18 kn Draw shear force and Bending moment Diagram Ma. moment at = L/2 then wl M = 2 M ma = L 2 wl 8 2 w 2 L 2 2

26 Eample 3 Eample 3 Draw shear force and Bending moment Diagram

27 S.F.D B.M.D

28 Eample 5 Draw shear force and Bending moment Diagram 2 = 14 = 7 M S = M M = 49 14(3.5) + 14(7)

29 Eample 6a Draw shear force and Bending moment Diagram S.F.D B.M.D

30 Eample 6b Draw shear force and Bending moment Diagram S.F.D B.M.D

31 Eample 6c Draw shear force and Bending moment Diagram S.F.D BMD B.M.D

32 Eample 6d Eample 6d Draw shear force and Bending moment Diagram

33

34

35 Group Work Draw shear force and Bending moment Diagram

36

37 Eample 1 Draw shear force and Bending moment Diagram

38 V(kN)

39 Eample 2 Draw shear force and Bending moment Diagram

40 +

41 Eample 2 Draw shear force and Bending moment Diagram

42 Eample 3 Draw shear force and Bending moment Diagram

43

44 Eample 4 Draw shear force and Bending moment Diagram

45 + + +

46 Problem 1 Draw shear force and Bending moment Diagram

47

48 Problem 2 Draw shear force and Bending moment Diagram

49 2 3 at 5 = M M V = 2 = 0 ( R = A = 3.46 m ) = 2 3 (3.46)(5)

50 Eample 1 Draw shear force and Bending moment Diagram Hinge

51 Reaction Calculation ( ) k A A M y left B (5) 10 0 = + = Reaction Calculation k C C M k A y y E y (32) 20(27) 5(16) 18(6) (12) 0 4 = = = = k E E E F y F 0 0 y = = = = E y 6k =

52

53 Frames (Eample 1) Draw Bending moment Diagram

54 Support reaction & Free Body diagram

55

56 S.F.D B.M.D

57 + S.F.D - - BMD B.M.D

58 Frames (Eample 2) Draw shear force and Bending moment Diagram

59

60 + N.F.D + _ S.F.D NFD N.F.D SFD S.F.D BMD B.M.D B.M.D N.F.D -

61 Frames (Eample 3) Draw shear force and Bending moment Diagram

62

63 N.F.D S.F.D B.M.D - - -

64 _ N.F.D S.F.D + B.M.D 251.6

65 N.F.D S.F.D B.M.D 168

66 S.F.D _ _ _ _ B.M.D

67 Frames (Eample 4) Draw shear force and Bending moment Diagram

68

69

70 S.F.D B.M.D + +

71 _ S.F.D + B.M.D

72 Frames (Eample 5) Draw shear force and Bending moment Diagram

73

74 Frames (Eample 6) Draw shear force and Bending moment Diagram

75

76 N.F.D S.F.D B.M.D _

77 _ N.F.D + _ + S.F.D _ + _ B.M.D

78 B.M.D S.F.D N.F.D _ + _

79 Frames (Eample 7) Draw Normal force, shear force and Bending moment Diagram

80 10kN/m 60kN o

81 NFD N.F.D SFD S.F.D BMD B.M.D S.F.D B.M.D

82 N.F.D S.F.D B.M.D

83 BMD B.M.D

84 Moment diagram constructed by the Eample 1 method of superposition

85

86

87 Eample 2.a

88

89 Eample 2.b

90

91 Problem 1 Draw Normal force, shear force and Bending moment Diagram

92 Problem 2 Draw Normal force, shear force and Bending moment Diagram

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