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Shear Stress in Rectangular & Circular Section

This document discusses shear stress in rectangular and circular cross-sections. It defines shear stress as the stress that acts parallel to the cross-section of a material due to shear forces. The equations for calculating shear stress are provided. For a rectangular beam cross-section, the shear stress distribution forms a parabolic curve where the maximum shear stress occurs at the neutral axis. The maximum shear stress is 1.5 times the average shear stress for a rectangular section and 4/3 times for a circular section. Hollow rectangular and circular cross-sections are also discussed briefly.

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Baldev Makwana
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1K views16 pages

Shear Stress in Rectangular & Circular Section

This document discusses shear stress in rectangular and circular cross-sections. It defines shear stress as the stress that acts parallel to the cross-section of a material due to shear forces. The equations for calculating shear stress are provided. For a rectangular beam cross-section, the shear stress distribution forms a parabolic curve where the maximum shear stress occurs at the neutral axis. The maximum shear stress is 1.5 times the average shear stress for a rectangular section and 4/3 times for a circular section. Hollow rectangular and circular cross-sections are also discussed briefly.

Uploaded by

Baldev Makwana
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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Shear stress In rectangular &

circular section
Prepare by : Department:
MAKWANA DHRUV V. - 216490319108 Mechanical
ABHISHEK MISHRA - 216490319109 Sem :
PARMAR HARDIK J. - 216490319110 3
MAKWANA BALDEV D. - 216490319112 Division :
B
Content

• Introduction
• Equation
• Shear stress distribution diagram
• Maximum & minimum shear stress relation
Shear force :
Shear force is a force acting in a
direction that’s parallel to (over the
top of) a surface or cross section of
a body, like the pressure of air flow
over an airplane wing. The word
shear in the term is a reference to
the fact that such a force can cut,
or shear, through the surface or
object under strain.
Shear stress :
Shearing Stress is defined as: “A
type of stress that acts coplanar
with cross section of material.”
Shear stress arises due to shear
forces. They are the pair of
forces acting on opposite sides
of a body with the same
magnitude and opposite
direction.
Equation of shear stress :
The ratio of applied force and
cross section area is called
shear stress.

It’s unit is Pascal.


Shear stress in beam :
When a beam is subjected to
nonuniform bending, both bending
moments, M, and shear forces, V,
act on the cross section. The normal
stresses, σx, associated with the
bending moments are obtained
from the flexure formula.
Shear stress Formula :
T = shear stress
F = shear force
A = cross sectional area
Y= distance from shear area To
neutral axis
I = moment of inertia
b = depth/2
Shear stress :
Shear stress :
At any cross-section of a beam, the two actions
to be resisted are the bending moment and the
shear force. At any point in the cross section of
a beam, the stress set up to resist the bending
moment is called bending stress, while the
stress resist shear force is called shear stress.
Let M and F be the bending moment and shear
force at a given section X-X of t beam shown in
Fig. Let f be the bending stress at a given point
in the s induced due to M. The bending stress f
is compressive or tensile depending upon
position with regard to neutral axis.
Let Tv be the vertical shear stress produced in the section due to application
vertical shear force F. We know that shear stress across a given plane is a
accompanied by complimentary shear stress of the same value but opposite in r The
vertical shear stress (Tv )(clockwise here) at the point across the vertical cross
section must therefore be accompanied by a horizontal shear stress (Tv) of the
same magnitude but opposite (anticlockwise) in nature.

Let, Tv = Tv = T numerically.

Let us now consider the top and bottom faces of the cross section. The horizontal
shear stresses on the top and bottom faces must vanish because there are no stress
on the outer faces of the beam. Since, the horizontal and vertical shear stresses at a
level must be equal, we arrive at a very interesting and important conclusion that t
vertical shear stress must be zero at the top and bottom,
So here
T = 0 and y=+d/2 or – d/2.
Shear stress distribution diagram:

The distribution of shearing stress on the cross-section


of the beam represents a parabolic curve where the
maximum shearing stress occurs at the neutral axis of
the beam.
Maximum shear stress is on neutral axis and minimum
shear stress is on edges.
• Rectangular section : T max = 1.5
• Circular section :
T max = 4/3
• Hollo rectangular section
1. Hollo circular section
Thank you

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