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Shear Force Diagram
• By• Monija Ahmed
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What is Shear Force?
• Shear force is a force that acts on a substance in a direction which is perpendicular to the extension of that substance
• Force instance the pressure of air down the border of an airplane wing. Shear forces frequently result in shear strain.
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Definition of SFD
• If the variation of V (Shear) is written as functions of position, x, and plotted, the resulting graphs are called the shear force diagram
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Implementations
• Shear Force Diagrams are analytical tools which help to perform structural design.
• These diagrams can be used to easily determine the type , size and material of member in a structure.
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• Deflection of a beam can be determined with the help of these diagrams.
• Bending moment diagram can be drawn from SFD as well.
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Convention to draw SFD
• Engineers have adopted a standard convention to draw SFD & use them in design practice. The convention is—
• Shear that produces clockwise moment is positive & anti-clockwise is negative
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Method
• The are 2 methods for drawing shear force diagram:
• 1) the basic method
• 2) the integration method
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• The basic method is used when a beam may be subjected to a loading that is a fairly complicated function.
• In other case, many problems require only the maximum values of shear and moment, and the location at which this values occur. The graphical method is most useful for these situations
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Steps for Basic Method
• 1) Determine the support reactions for the beam. • 2) Specify an origin for a co-ordinate x along the length
of the beam. • 3) Section the beam with an imaginary cut at a distance
x, and draw the free-body diagram. • 4) Determine shear and bending moment as a function
of x using equilibrium equations. • 5) Repeat steps 3 and 4 for all regions between any two
discontinuities of loading. • 6) Draw, to scale, the functions on a sketch of the beam.
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Example-1
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• concentrated loads • consider a simply support beam AB • with a concentrated load P • RA = P b / L RB = P a / L • for 0 < x < a • V = RA = P b / L • for a < x < L • V = RA - P = - P a / L •
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Example-2
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• an overhanging beam is subjected to a • uniform load of q = 1 kN/m on AB • and a couple M0 = 12 kN-m on midpoint • of BC, construct the shear for • the beam Soln- RB = 5.25 kN RC = 1.25 kN • shear force diagram • V = - q x on AB • V = constant on BC
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Example-3
• A constant load of ωo per unit length is applied on a simply supported beam as shown below. Draw the shear force and bending moment diagram
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Σ Fx=0=> RAx=0
By symmetry,RAy=RBy= ωoL/2
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Σ Fx=0=> V= ωoL/2-ωox
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Example-4A beam with a hinge is loaded as above
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• Σ Fx=0=> RAx=0• MB=0 => RAy X2=0=> RAy=0• Σ MD=0=> 10 X 5 X 5 X 4 X 2= RCy X 4• RCy= 22.5 kN• RDy= 10+5X4-22.5=7.5 kN
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•Thank you