TRANSVERSE SHEAR IN BEAMS 1

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TRANSVERSE SHEAR IN BEAMS - 1 (7.1 7.3)
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Origin of Shear Forces in Beams Under Transverse
Loading
Transverse load applied to beam made up of three
boards
Boards free to slip
Horizontal force in bond keeps boards from
slipping
The horizontal force opposes the shearing
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Introduction

• Longitudinal shearing stresses must exist in any
  member subjected to transverse loading.

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Shear on the Horizontal Face of a Beam Element

• Consider prismatic beam

(Horizontal force)
(First moment of area)
(Force/unit length)
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Shear on the Horizontal Face of a Beam Element
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Determination of the Shearing Stress in a Beam
t

• If the width of the beam is comparable or large
  relative to its depth, the shearing stresses at
  D1 and D2 are significantly higher than at D.

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Shearing Stresses txy in Common Types of Beams
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Shearing Stresses txy in Common Types of Beams
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Further Discussion of the Distribution of
Stresses in a Narrow Rectangular Beam

• Shearing stresses are independent of the distance
  from the point of application of the load.

• Normal strains and normal stresses are unaffected
  by the shearing stresses.

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Sample

• SOLUTION
• Develop shear and bending moment diagrams.
  Identify the maximums.

• Determine the beam depth based on allowable
  normal stress.

A timber beam is to support the three
concentrated loads shown. Knowing that for the
grade of timber used,

• Determine the beam depth based on allowable shear
  stress.

• Required beam depth is equal to the larger of the
  two depths found.

determine the minimum required depth d of the
beam.
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Sample
SOLUTION Develop shear and bending moment
diagrams. Identify the maximums.
12
Sample