This document discusses strength of materials concepts related to shear force diagrams (SFD) and bending moment diagrams (BMD) for beams. It defines key terms like shear force, bending moment, and point of contraflexure. It also explains how to draw SFDs and BMDs for different beam types under various loading conditions and the relationships between loading, shear force, and bending moment. Application of the diagrams to reinforcement design is also mentioned.

1. STRENGTH OF MATERIALS
SFD AND BMD
key points

2. SFD & BMD FOR BEAMS
 Types of BEAMS
 Types of LOADS
1. Point loads
2. Uniformly distributed load
3. Uniformly varying load
4. Couple
 Concept of shear force and bending moment
 S.F and B.M diagrams for
1. Cantilever
2. Simply supported including overhanging
 Point of contraflexure
 Relation between S.F., B.M and rate of loading at a
section of a beam.

3. Beam - Definition
Beam
 is the horizontal member of a structure
 carrying transverse loads
 transfer all the loads including its self-weight to the
columns or walls.
Transverse Load
 perpendicular to longitudinal axis of beam

4. https://www.youtube.com/watch?v=5K27dJqGpf8

5. Moment and Bending moment
Moment:
 It is the product of force and perpendicular
distance between line of action of the force and
the point about which moment is required to be
calculated.
Bending Moment (BM):
 The moment which causes the bending effect
on the beam is called Bending Moment. It is
generally denoted by ‘M’ or ‘BM’.

6. Shear Force and Bending Moment
Shear force at a section:
 The algebraic sum of the vertical forces acting
on the beam either to the left or right of the
section.
Bending moment (BM) at section:
 The algebraic sum of the moments of all
forces acting on the beam either to the left or
right of the section

7. What the BM does to the beam

8. Shear Force and Bending Moment Diagrams
SFD:
The diagram which shows the variation of shear
force along the length of the beam is called Shear
Force Diagram (SFD).
BMD:
The diagram which along the length shows the
variation of bending moment of the beam is called
Bending Moment Diagram (BMD).

9. Sign Conversion for S.F
F
F
F
F
+ ve shear
force
- ve shear force

10. Sign Convension for B.M
Sagging B.M
 The bending moment that tends to bend the beam to
a curvature having convexity at the bottom
 Sagging Bending Moment is considered as positive
bending moment.
Convexity

11. Sign Conversion for B.M Cont…
Hogging B.M
 Bending moment that tends to bend the beam to a
curvature having convexity at the top.
 Hogging Bending Moment is considered as Negative
Bending Moment
Convexity

12. Application of SFD & BMD
 To know the exact placement of
reinforcement in the structure to counteracts
the force and moment.
 for shear - stirrups are used in lateral direction
 For bending - bars are used in longitudinal
direction

13. Point of Contra flexure :
 It is the point on the bending moment
diagram where B.M changes the sign from
+ve to –ve or vice versa.

14. Important points for drawing SFD and BMD
1. Length of S.F.D and B.M.D must be equal to the
span of the beam.
2. S.F.D is drawn below the loaded beam and B.M.D
is drawn below S.F.D
3. For Simply supported beam B.M is zero at the
supports.
4. For cantilever beam B.M will be zero at free end.
5. Calculate S.F and B.M at all critical points
6. If no load is present between two points, then S.F
will be constant.
7. Consider the left or right side portion of the section

15. Important points for drawing SFD and BMD
Cont…
8. Add the forces (including reaction) normal to the
beam on one of the portion. (By considering sign
conversion)
9. The positive values of S.F and B.M are plotted
above the base line and Negative values below the
base line
10. The S.F.D will increase or degrease suddenly i.e.
by a vertical straight line at a section where there is
a vertical point load.
11. The S.F between any two vertical loads will be
constant and hence the S.F.D between two vertical
loads will be horizontal.

16. Relationship Between w, F, and M
 Rate of change of shear force is equal to rate of
loading
dF/dx = w
 Rate of change of bending moment is equal to
shear force
dM/dx = F