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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
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.
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
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.
Continue…
› Deflection of a beam can be determined with the help of these diagrams.
› Bending moment diagram can be drawn from SFD as well.
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
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 -
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
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.
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.
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
S.F Calculation
FA left = 0FA Right = 66kNFC = 66-(204) = -14kNFD left= -14kNFD Right=(-14)-10=-24kNFB Left = -24 kNFB Right= -24 + 24 = 0kN
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.
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
S.F Calculation
FA Left = 0kNFA Right= -2 kNFB = -2-0 = -2kNFC = -2-8 = -10FD = -10
Example On Overhanging BeamProblem 3 :-
Calculate the value and draw a bending moment and shear force diagram for following Overhanging beam shown in fig.
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
S.F Calculation
FA Left = 0kNFA Right = -10kNFC = -10kNFB Left = -10-35 = 25kNFD Right = 25kNFD Right = 25-25 = 0kN
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.
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
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
Thanks…
