10.01.03.083

Shear Force Diagram

• By• Monija Ahmed

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.

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.

• 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

Method

• The are 2 methods for drawing shear force diagram:

• 1) the basic method

• 2) the integration 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-1

• 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 •

Example-2

• 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

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

Σ Fx=0=> RAx=0

By symmetry,RAy=RBy= ωoL/2

Σ Fx=0=> V= ωoL/2-ωox

Example-4A beam with a hinge is loaded as above

• 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

•Thank you