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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