Pure Bending of Straight Symmetrical Beams

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Pure Bending of Straight Symmetrical Beams

• Linear bending stress distribution, and no shear
  stress (Fig. 4.3)
• Neutral axis passes through centroid of
  cross-section
• Section modulus, ZI/c, used for the case when
  the neutral axis is also a symmetry axis for the
  cross-section
• Table 4.2 for properties of plane sections
• Restrictions to straight, homogeneous beams
  loaded in elastic range and cutting planes
  sufficiently far from discontinuities

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Bending of Straight Symmetrical Beams Under
Transverse Forces

• Any cut cross-section loaded by two types of
  stresses (if no torsion occurs)
• Bending stress as in case of pure bending
• Transverse shear stresses
• Direct and transverse shear stress
• Direct average shear stress in pin and clevis
  joint (Fig. 4.4) is smaller than maximum stress
• Non-linear distributions are caused in reality by
  stiffnesses and fits between mating members, etc.

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Transverse Shear Stress Equations

• Bending of laminated beam explains existence of
  transverse shear (Fig. 4.5)
• Beam loaded in a vertical plane of symmetry
• Elemental slab in equilibrium under differential
  bending and shear forces (Fig. 4.6)
• Derived equation valid for any cross-sectional
  shape
• Expressed in terms of moment of area about
  neutral axis, leading to the area moment method
  for calculating transverse shearing stresses
• Irregular cross-sections can be divided into
  regular parts (4-25)

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Transverse Shear Stress Equations
Stress distribution in section at z at distance
y1 from neutral axis
Area Moment method for calculating transverse
shear stresses
Irregular Cross-Section
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Conclusions on Transverse Shearing Stress
Calculations

• Maximum Value at Neutral Axis
• Depends on Shape of Cross Section (Table 4.3)
• Equal to Zero at Top and Bottom Boundaries
• Important for Short Beams
• Wood Beams if span/depth lt 24
• Metal Beams with Thin Webs- if span/depthlt15
• Metal Beams with Solid Section-if span/depthlt8

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MAE 343-Intermediate Mechanics of
MaterialsHomework No. 2 - Thursday, Sep. 02,
2004
        1) Textbook problems required on
Thursday, Sep. 9, 2004  
Problems 4.10 and 4.15     2)
Textbook problems recommended for practice before
Sep. 9, 2004   Problems 4.7 4.18
(except 4.10 and 4.15)