shear force diagram and its exampls
TRANSCRIPT
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Year: 2016-17 Subject: Mechanics of Solid (2130003)
Topic: Shear force bending moment
Name of the Students:Kansara Sagar 160283105004Makvana Yogesh 160283105005Padhiyar Shambhu 160283105006Sindhav Jaydrath 160283105011Vasava Yogesh 160283105012
Gujarat Technological University L.D. College of Engineering
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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.
› Unit of S.F is N or kN.
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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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Continue…
› 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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Sign Convention
• The Shear Force is positive if it tends to rotate the beam section clockwise with respect to a point inside the beam section.
Positive S.F. Negative S.F.
F +
F +
F -
F -
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The Basic Method› 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 on simply supported beam
Problem 1 :- Calculate the value and draw a
bending moment and shear force diagram for following beam shown in fig.
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Solution Problem 1
Solution:-
The beam has two unknown reaction Ay and By. Ay + By = 90……… (1)Taking moment from Ay
By10 = (20 42)+(10 8)By = 240/10
By = 24kN Ay = 90-24 = 66kN
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S.F Calculation
FA left = 0FA Right = 66kNFC = 66-(204) = -14kNFD left= -14kNFD Right=(-14)-10=-24kNFB Left = -24 kNFB Right= -24 + 24 = 0kN
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Example On Cantilever Beam
Problem 2 :-
Calculate the value and draw a bending moment and shear force diagram for following cantilever beam shown in fig.
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Solution Problem 2
The support reaction for given beam can be easily determined by following method.
Dy = (42 1/2) + (2 4)
Dy =10 kN
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S.F Calculation
FA Left = 0kNFA Right= -2 kNFB = -2-0 = -2kNFC = -2-8 = -10FD = -10
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Example On Overhanging BeamProblem 3 :-
Calculate the value and draw a bending moment and shear force diagram for following Overhanging beam shown in fig.
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Solution Problem 3
Applying equation of static equilibrium.
Ay - By = 45kN
Taking Moment Of ABy6 =(2510)+(5 4 4) By = (250+80)/6 = 55kN Ay = -10Kn
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S.F Calculation
FA Left = 0kNFA Right = -10kNFC = -10kNFB Left = -10-35 = 25kNFD Right = 25kNFD Right = 25-25 = 0kN
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Example On Overhanging Beam with Point of Contraflexure
Problem 4 :-
Calculate the value and draw a bending moment and shear force diagram for following beam shown in fig also find the point of contraflexure.
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Solution Problem 4The support reaction
can be find as following
Ay+Cy=(104)+20 =60kN
Taking moment from ACy8=(1042)+(20 10)Cy=280/8=35kNAy=60-35 = 25kN
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S.F Calculation
FA left=0FA right=25kNFB=25-(10 4)= -15 kNFC left= -15 kNFC right=25-5=20kNFD left=20kNFD right=20-20=0kN
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Thanks…