1-80 Section 1Shear Stresses in Beams Transverse loads on beams are common, and they cause transverse and complementary longitudinal shear stresses in the beams.. Schematically, the tran
Trang 11-80 Section 1
Shear Stresses in Beams
Transverse loads on beams are common, and they cause transverse and complementary longitudinal shear stresses in the beams Schematically, the transverse shear stresses are distributed on a rectangular cross section as shown in Figure 1.5.20 The shear stress is zero at free surfaces by definition
The internal shear stress is calculated according to Figure 1.5.20 from
(1.5.30)
where τ = shear stress value at any point on the line , – , at a distance y′ from the neutral axis
V = total shear force on cross-sectional area A
Q = A′ = area above line , – ,; = distance from neutral axis to centroid of A′
I = moment of inertia of entire area A about neutral axis
t = width of cross section where τ is to be determined
This shear formula gives τmax = 1.5 V/A if t is constant for the whole section (rectangle).
Note that the magnitude of the shear stress distribution changes sharply where there is an abrupt
change in width t, such as in an I-beam, Figure 1.5.21.
Shear Flow
In the analysis of built-up members, such as welded, bolted, nailed, or glued box beams and channels,
a useful quantity is the shear flow q measured in force per unit length along the beam,
(1.5.31)
FIGURE 1.5.20 Transverse shear stress distribution.
FIGURE 1.5.21 Shear stress distribution for I-beam.
τ =VQ
It
′ ′
I
=