2. Unit 2- Stresses in Beams
Lecture -1 – Review of shear force and bending
moment diagram
Lecture -2 – Bending stresses in beams
Lecture -3 – Shear stresses in beams
Lecture -4- Deflection in beams
Lecture -5 – Torsion in solid and hollow shafts.
Topics Covered
3. Shear Stresses in Beams of
Rectangular Cross Section
In the previous chapter we examined the case
of a beam subjected to pure bending i.e. a
constant moment along axis .
When a beam is in pure bending, the only
stress resultants are the bending moments and
the only stresses are the normal stresses acting
on the cross sections.
Most beams are subjected to loads that
produce both bending moments and shear
forces (non-uniform bending)
4. Shear Stresses in Beams of
Rectangular Cross Section
In these cases, both
normal and shear forces
are developed in the
beam.
Normal stresses are
calculated with the
Flexure Formula.
We will now look at the
Shear Stresses
5. Vertical & Horizontal
Shear Stresses
Consider a beam of rectangular cross section subjected
to a positive shear force.
6. Shear Stresses
τ = F ×
A y
−
I × b
x
σ +dσ
M M+dM
σ
b
y1
Area A
€
dM
I
× A × y
−
dx
€
y
−
B
A C
D
Shear forces and bending moments are
different across different sections.
7. Shear stress distribution
for different section
A is the area of the x-section cut off by a line
parallel to the neutral axis. is the distance of
the centroid of A from the neutral axis
Rectangular Section
Parabolic distribution of
shear stresses
8. Shear stress distribution
for different section
The maximum value of shear stress would
obviously beat the location y = 0.
Rectangular Section
