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

## 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).
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Shear Stresses In Beams

SHEAR STRESS DISTRIBUTION

(i) Rectangular Beam • 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, Where S = SF at the section = 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. and 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 t avg= t local  (iii) Triangular Section • Shear stress at a distance y form vortex is given by • Maximum shear stress exists at y = h/2 (at the middle of triangle) and is given by • Average shear stress is given by • Shear stress at N.A. is given by (iv) Diamond Section • Shear stress at level PQ is given by • Shear stress at N.A. • Average shear stress = Hence ζn.a. = ζavg

• Maximum shear stress occurs at 3/8 d form top and bottom or d/8 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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## Civil Engineering SSC JE (Technical)

113 docs|50 tests

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