shear and bending moment diagram
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Shear and Bending Moment Diagram
Summer 2020Dr. Akm Rahman
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Cantilever Beam
Simply Supported Beam
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Beam Types
Concentrated Load
Cantilever beam-Diving board,Balcony,Aircraft Wing
Overhanging Beam-Brooklyn Bridge
Bridge
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Types of Loads
Steel beamw=Weight of beam per unit length,
Lb/ft, N/m
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Take moment at point B, MB Ra*40=40*20+5*8So, Ra=21 kip
Take all the forces in Y dir--- Ra+Rb=40+5, So Rb=45-21=24 kip
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Take Moment at point B,-Ra*8+60*7.5+20*5+30*3=0Ra=80 kN=80,000 N
Moment=load*vertical distance
Rb=?=30 kN
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We Will learn Reaction,Shear &Moment Diagram
Ra=49.2 kN
49.2 kN19.2 kN
-57.1 kN
Shear Diagram
M at 3 m--49.2*3=147.6 kN.MM at 8.5 m… 49.2*8.5-30*5.5=253.2 kn.MM at 12 m… =0
147.6 kN.m
X=0 X=3 X=8.5
253.2 kn.M
X=12 Moment Diagram
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V=Shear force=force acting parallel to the beam section
Shear Force
Shear Force Diagram= Shear force along the length
V=42.9 kNM=42.9*2 kN.m=98.4
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Shear force , V is internal force; internal resistance to external force
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Now consider bending moment
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V=49.2-30=19.2 kN
M=49.2*5-30*2=186 KN.M
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V=42.9-30-70=-57.1 kN
M=171.1 kN.m
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Take moment at A,Rb=(10*4+24*6)/12=15.33 KipRa=18.67 kip
Load Diagram
Find Shear and Moment Diagram
V at left of x=4 … 18.67-w*x=18.67-2*4=10.67 kip
Right of x =4… 10.67-10=.67 kipV at x= 6… 18.67-10-w*x=-3.33 kip
w=2 kip/ft
X=0 X=4 X=12
18.67 kip10.67 kip
.67 kip -3.33 kip
-15.33 kip
M at left of x =4..18.67*4-w.x^2/2=58.68 kip.ft
Shear and Moment Diagram in the next page
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