Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Civil Engineering SSC JE (Technical)

Civil Engineering (CE) : Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

The document Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

Shear Stresses In Beams

SHEAR STRESS DISTRIBUTION

(i) Rectangular Beam

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • The intensity of shear at a fiber on the plane of cross-section located.the level of EF at a distance y form the neutral axis is given by,

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Where S = SF at the section
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev = 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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  •  Average shear stress is given by

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Hence 
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

(ii) Solid Circular Section

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Average shear stress is given by

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Hence
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

(iii) Triangular Section

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Maximum shear stress exists at y = h/2 (at the middle of triangle) and is given by

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Average shear stress is given by

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Shear stress at N.A.

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
is given by

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

(iv) Diamond Section

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Shear stress at level PQ is given by

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Shear stress at N.A.

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Average shear stress =

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Hence ζn.a. = ζavg

  • Maximum shear stress occurs at 3/8 d form top and bottom or d/8 form neutral axis

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Hence 
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

(V) I Section

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Shear Stress distribution in flange:

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Shear stress distribution within the web

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

  • Shear stress distribution in some other  section:

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

CORE OF SECTIONS OF DIFFERENT SHAPES

1. Rectangular Section In order that tension may not develop, we have the condition

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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 
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
.
For a rectangular section of width b and depth d.

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
and A = b.d.
Hence Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Substituting this value of k, we get

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev
or Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

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

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev 

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,

 Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

Hence the core for a hollow circular section is a concentric circle of diameter 
Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

where d = inner diameter, D = outer diameter.

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Sample Paper

,

Free

,

pdf

,

study material

,

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

,

video lectures

,

ppt

,

Exam

,

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

,

practice quizzes

,

Previous Year Questions with Solutions

,

MCQs

,

Objective type Questions

,

Shear Stresses In Beams Civil Engineering (CE) Notes | EduRev

,

Important questions

,

past year papers

,

Semester Notes

,

Summary

,

Extra Questions

,

mock tests for examination

,

shortcuts and tricks

,

Viva Questions

;