The document discusses transverse loading on beams and stress in beams. It defines different types of beams including cantilever, simply supported, overhanging, and continuous beams. It also defines types of loads such as point loads and uniformly distributed loads. It explains shear force as the sum of vertical forces on one side of a point on the beam. Bending moment is defined as the sum of moments due to vertical forces. Shear force diagrams and bending moment diagrams are used to show shear force and bending moment at every section of the beam due to transverse loading. An example problem is provided to illustrate calculating and drawing the shear force and bending moment diagrams for a cantilever beam with a point load.

1. STRENGTH OF MATERIALS
Dr.S.SURESH,
Assistant Professor,
Department of Mechanical Engineering.
UNIT-II
TRANSVERSE LOADING ON BEAMS AND
STRESS IN BEAM

2. Beams
Types of beams
Types of loads
Shear force and bending moment
SFD & BMD

3. BEAMS
 Structural element
 Resist loads which perpendicular to the their
axis

5. TYPES OF BEAM

6. CANTILEVER BEAM
SIMPLY SUPPORTED BEAM

7. OVER HANGING BEAM
CONTINUOUS BEAM

8. TYPES OF LOADS

9. Point Load
UDL

11. SHEAR FORCE
 The shear force at any point along a loaded beam
may be defined as the algebraic sum of all vertical
forces acting on either side of the point on the beam.

12. BENDING MOMENT
 Bending moment at any point along a loaded beam
may be defined as the sum of the moments due to all
vertical forces acting on either side of the point on
the beam.

13. SHEAR FORCE AND BENDING MOMENT
DIAGRAMS
 A shear force diagram (SFD) which shows the shear
force at every section of the beam due to transverse
loading on it.
 A bending moment diagram (BMD) is a diagram which
shows the bending moment at every section of the beam
due to transverse loading on it.

15. Shear Force Calculation
SF at B = 1.5 KN
SF at C = 1.5 + 2 = 3.5 KN
SF at A = 1.5 + 2 = 3.5 KN
Bending Moment Calculation
BM at B = 0
BM at C = -1.5 x 0.5 = -0.75 KN-m
BM at A = (-1.5 x 1.5) + (-2 x 1) = -4.25 KN-m
1. Draw Shear force and Bending moment diagram for a
cantilever beam of span 1.5 m carried point load as
shown in Fig.

16. EXAMPLE

18.  Shear Force calculation
SF at B = 0
SF at C = 1x1.5 =1.5 KN
SF at A = 1.5 KN
 Bending Moment calculation
BM at B = 0
BM at C = 1x1.5x(1.5/2) =1.125 KN
BM at A = 1x1.5x(1.5/2 + 0.5)
=1.875 KN
A Cantilever of length 2.0 carries a uniformly distributed load of 1 KN/m
run over a length of 1.5 m from the free end. Draw the shear force and
bending moment diagrams for the cantilever.

19.  Find the reactions at A & B
1.Taking moment at A
2. Sum of forces upwards = Sum of forces downwards

20.  SF Calculation
SF at B = -W/2
SF at C = -W/2 + W
= +W/2
 BM Calculation
BM at B = 0
SF at C = W/2 x L/2
= WL/4
BM at A = 0
Note:

22. SHEAR FORCE
BENDING MOMENT

23. REACTIONS AT A & B
Shear Force
SF at B = -0.5 wl
SF at C = -0.5 wl + w (l/2)
= 0
SF at A = +o.5wl
Bending Moment
BM at B = 0
SF at C = 0.5 wl (l) - w (l/2)
(l/4)
= wl2/8
SF at A = 0

25. SHEAR FORCE CALCULATION
SF at B = - 50 KN
SF at D = -50 + 40 = -10 KN
SF at C = -50 + 40 + (10 x 4) = +30 KN (Without Point Load)
SF at C = 30 + 50 = +80 KN
SF at A = +80 KN
SF at E = -RB + 40 + 10 (x-4)
0 = -50 + 40 + 10 (x-4)
X = 5 m