Shear Stresses in Beams

# Shear Stresses in Beams Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

## Document Description: Shear Stresses in Beams for Mechanical Engineering 2022 is part of Strength of Materials (SOM) for Mechanical Engineering SSC JE (Technical) preparation. The notes and questions for Shear Stresses in Beams have been prepared according to the Mechanical Engineering exam syllabus. Information about Shear Stresses in Beams covers topics like and Shear Stresses in Beams Example, for Mechanical Engineering 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Shear Stresses in Beams.

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SHEAR STRESSES IN BEAMS
(ii) Solid Circular Section

• The shear stress at a fibre on the plane of cross-section located at a distance y from
neutral axis is given by

moment of the area above
EF y = distance form neutral axis.
I = moment of inertia about
N.A. b = width of the beam at the level EF

• Shear stress in terms of y form N.A. is given by

• Average shear stress is given by

• Maximum shear stress occurs at the N.A. & is given by

Hence

• The distance from N.A. at which the average shear  stress is equal to the local shear stress

(ii) Solid Circular Section

• The shear stress at a fibre on the plane of cross-section located at a distance y from neutral axis is given by

• Maximum shear stress  occurs at the N.A. & is given by

• Average shear stress is given by

Hence

• The distance from N.A. at which the local shear stress is equal to average shear stress is given by

(iii) Triangular Section

• Shear stress at a distance y form vortex is given by

• Maximum shear stress exists at  (at the middle of triangle) and is given by

• Average shear stress is given by

•  Shear stress at N.A.  form top  is given by

(iv) Diamond Section

• Shear stress at level PQ is given by

• Shear stress at N.A.

• Average shear stress =

Hence tn.a. = tavg

• Maximum shear stress occurs at  form top and bottom or  form neutral axis

Hence
(V) I Section

• Shear Stress distribution in flange:

• Shear stress at the junction of flange & web, but within the flange.

• Shear stress distribution within the web

• Maximum shear stress exists at N.A. and is given by

• Shear stress at the junction of web and flange but within the web

Shear stress distribution in some other section:

CORE OF SECTIONS OF DIFFERENT SHAPES
1. Rectangular Section
In order that tension may not develop, we have the condition

wherek = radius of gyration of the section with respect to the NA
d = depth of the section
Thus, for not tension in the section, the eccentricity must not exceed

For a rectangular section of width b and depth d.

and A = b.d.
Hence

Substituting this value of k, we get

or
Thus the stress will be wholly compressive throughout the section, if the line of action of P falls within the rhombus (as shaded portion of figure), the diagonals of which are of length d/3 and b/3 respectively. This rhombus is called the core or kern of the rectangular section.

2. Solid Circular Section

The core of a solid circular section is a circle, with the same centre, and diameter d/4.

3. Hollow Circular Section
For a hollow circular section,
Hence the core for a hollow circular section is a concentric circle of diameter

where d = inner diameter,
D = outer diameter.

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