SHEAR FORCE AND BENDING MOMENT DIAGRAMS CLASS NOTES
SHEAR FORCE AND BENDING
MOMENT DIAGRAMS CLASS
NOTES
Shear force and bending moment
diagrams are graphical method to find
their maximum values and their point of
acting. Firstly, design the beam for
maximum moment alone. Secondly
design beam for maximum shear force.
Among the two designs, larger values of
beam becomes the final design. It
satisfies for maximum conditions of
shear force and bending moment.
DEFINITION OF A BEAM
Beam is a most important member of a machine, vehicle or a structure.
(i) Normally it is horizontal but it can be in any orientation. It can be at any angle with the horizontal.
(ii) All loads must be perpendicular to the length of the beam. Such perpendicular loads on beam are lateral loads or transverse loads.
(iii) For an inclined load, consider component perpendicular to the length.
(iv) Width and depth are small as compared to the length of the beam.
TYPES OF BEAMS
Types of beams are as per type of supports, number of supports and types of load.
(i) Simply supported beam
Support beam on rollers/wheels/rockers.
(ii) Cantilever beam
One end fixed and the other end free.
(iii) Hinged beam
There is a pin connection at one end. Use two pins if hinged at both ends. Pinned ended beam/pivoted ended beam/hinged ended beam are the same thing.
(iv) Continuous beam
When number of supports is greater than two.
(v) Overhanging beam
A beam not supported on the ends has left overhang and right overhang or both. These overhangs may be equal or unequal.
(v) Fixed beam
Fix beam at both ends.
(vii) DETERMINATE BEAMS
Find unknown reactions from the equations of equilibrium.
(viii) INDETERMINATE BEAMS
Unknown reactions are non determinate from the equations of equilibrium.
SPAN OF THE BEAM
The length of the beam is the SPAN.
INTRODUCTION
Find the followings graphically from Shear force diagram.
(i) Magnitude of absolute maximum shear force
(ii) Location of the absolute maximum shear force on the beam
1. SHEAR FORCE ON A BEAM
It is NET VERTICALLY UPWARDS FORCE OR NET VERTICALLY DOWNWARDS FORCE due to the forces acting on one side of the point. Find the shear force at various points on the beam, then draw the S.F.D.. From the loaded beam, find graphically absolutely maximum shear force and its location. Shear Force Diagram shows the variation of the shear force along the span of the beam.
1.1 STEPS TO DRAW THE SHEAR FORCE DIAGRAM
(i) Draw the Free Body Diagram.
(i) Remove the support (or supports)
(ii) Install reactions in place of supports.
Such a sketch of the beam with reactions and actual external loading is FREE BODY DIAGRAM. In the first step, DRAW THE FREE BODY DIAGRAM. Obtain the Free body diagram.
(ii) Install only perpendicular reactions in place of FREE SUPPORT(S).
(ii) Install two unknown reactions (one vertical and one horizontal reaction). These reactions are in place of a hinge or a Pin or a pivot support.
(iii) Install vertical reaction, horizontal reaction and a restoring moment in place of a fixed support. Fixed support is an encastered support or builtin support.

Determine the value of unknown reactions using the equations of equilibrium i.e.
(i) ΣF_{x} = 0
(ii) ΣF_{y} = 0
(iii) ΣM = 0
CAUTION: Use equation ΣM = 0 at any ONE END OF THE BEAM and not at any other point.

Now find the shear force at few locations on the beam. Use the definition of shear force on a beam.

Then plot the SFD

Find the magnitude of absolute maximum shear force

Find the location of the maximum shear force.
2. BENDING MOMENT ON A BEAM
It is the NET CLOCKWISE MOMENT OR NET ANTICLOCKWISE MOMENT due to all the forces acting on one side of the point. (Say on the beam at 1 m from the left end of the beam). Find the bending moment at various points on the beam & draw the BMD. From the BMD, find graphically the absolute maximum bending moment. (neglect the sign) . Also find the location of the absolute maximum moment.
Bending Moment Diagram is one which shows graphically the variation of the bending moment along the length of the beam.
2.1 STEPS TO DRAW THE BMD

Draw Free Body Diagram.

Remove the support (or supports) and install reactions in place of supports. Such sketch of beam with reactions and actual external loading is FREE BODY DIAGRAM. Therefore, in the first step, DRAW THE FREE BODY DIAGRAM.

Determine the value of unknown reactions using the equations of equilibrium i.e.
(i) ΣF_{x} = 0
(ii) ΣF_{y} = 0
(iii) ΣM = 0
CAUTION: Use equation ΣM = 0 at any ONE END OF THE BEAM and not at any other point.
4. Now find the bending moments at few locations on the beam. Use the definition of bending moment on a beam.
5. Then plot the BMD.
6. Find the magnitude of the absolute maximum bending moment.
7. Find the location of the absolute maximum moment.
SFD and BMD for loaded beams
Fig. Shear force & bending diagrams for a Cantilever
Fig.1 SSB WITH UDL
Fig. CANTILEVER BEAM WITH UDL & CONC LOADS
Fig. SSB WITH ONLY MOMENT AT 1 m FROM LH SUPPORT
BEAM DESIGN
Utility of SFD and BMD
Design the beam for maximum shear force.
Design means
(i) Select the material of construction
(ii) Select the method of manufacture
(iii) To select the shape and contour of the beam
(iv) To find the dimensions on the basis of
(a) Strength
(b) Stiffness
(c) Stability
(d) Wear
(v) To draw a detailed drawing showing the material of construction, method of manufacture, shape and configuration with dimensions.
(vi) All this help fabrication, installation and safe use the beam.
FINAL SELECTION OF THE BEAM
NOTE: Firstly design the beam for maximum shear force. Secondly design the beam for maximum bending moment. Bigger dimensions in the two designs are the final choice for the beam.
https://www.mesubjects.net/wpadmin/post.php?post=4231&action=edit MCQ SFD & BMD
https://mesubjects.net/wpadmin/post.php?post=3142&action=edit Q. ANS. SFD and BMD