2. 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, Z=I/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

7. 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.

10. 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)

11. 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

13. 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 < 24
Metal Beams with Thin Webs- if span/depth<15
Metal Beams with Solid Section-if span/depth<8

18. MAE 343-Intermediate Mechanics of Materials Homework No
MAE 343-Intermediate Mechanics of Materials Homework 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 – (except 4.10 and 4.15)