Chapter_07_3 - Chapter7 InternalForces 1 Objectives 1...

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03/16/10 Chapter 7 - Internal Forces 1 Chapter 7 Internal Forces
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03/16/10 Chapter 7 - Internal Forces 2 Objectives 1. To show how to use the method of sections  for determining the internal loadings in a  member 2. To generalize the procedure by formulating  equations that can be plotted so they  describe the internal shear and moment  throughout a member 3. To analyze the forces and study the  geometry of cables supporting a load
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03/16/10 Chapter 7 - Internal Forces 3 Relationship Between  Distributed Load, Shear Force  and Moments
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03/16/10 Chapter 7 - Internal Forces 4 M 1 F 2 F 1 M 2 w = w(x ) x w B C A D
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03/16/10 Chapter 7 - Internal Forces 5 V M V+ V M+ M F = w(x) x x
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03/16/10 Chapter 7 - Internal Forces 6 V M V+ V M+ M F=w(x) x x ( 29 y 2 F 0 V w(x) x (V V) 0 V w(x) x M 0 M V x w(x) x k x (M M) 0 M V x w(x)k x = + - ∆ - + ∆ = = - = - - ∆ + + + ∆ = = ∆ -
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03/16/10 Chapter 7 - Internal Forces 7 ( 29 limΔx 0 dV w(x) dx Slope of Neagative of distributed shear diagram load intensity Divide through by x = - =
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03/16/10 Chapter 7 - Internal Forces 8 ( 29 limΔx 0 dM V dx Slope of Shear moment diagram Divide through by x = =
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03/16/10 Chapter 7 - Internal Forces 9 C BC B C BC B V w(x)dx M Vdx = - = Changes in Shear and  Moment
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03/16/10 Chapter 7 - Internal Forces 10 Changes in Shear and  Moment 1. Change in shear between B and C is  equal to the negative of the area under  the distributed load curve between  those points. 2. Change in moment between B and C  is equal to the area under the shear  force curve between those points. 3. Does not apply if concentrated force or  couple is applied between B and C.
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03/16/10 Chapter 7 - Internal Forces 11 Force V V+ V F x ( 29 y F 0 V V V F 0 V F = - + ∆ - = = - Change in shear is negative  so shear diagram jumps  downward when F acts  downward
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03/16/10 Chapter 7 - Internal Forces 12 Moment M M+ M M O x ( 29 O O M 0 M M M M 0 M M = - + + ∆ - = = Change in moment is positive  so moment diagram jumps  upward when M O  acts  Clockwise.
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03/16/10 Chapter 7 - Internal Forces 13 Changes in Shear and  Moment 1. If w(x) is a polynomial of degree n, then  V(x) is a polynomial of degree n+1, and   M is a polynomial of degree n+2 2. w = 0 V=constant M=linear 3. w=constant V=linear M=quadratic 4. w=linear V=quadratic M=cubic
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03/16/10 Chapter 7 - Internal Forces 14 15 ft 150 lb/ft Draw V and M diagrams
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03/16/10 Chapter 7 - Internal Forces 15 15 ft 150 lb/ft Reactions 750 lb 375 lb x 15 150 ) x ( w =
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03/16/10 Chapter 7 - Internal Forces 16 15 ft 150 lb/ft 750 lb 375 lb x 15 150 ) x ( w = x
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Chapter_07_3 - Chapter7 InternalForces 1 Objectives 1...

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