Building Design and Construction Handbook - Merritt - Ventech!

STRUCTURAL THEORY 5.21
Since for these loading conditions, the unit stress is constant across the section,
the equation of equilibrium may be written
P � Aƒ (5.21)
where P � load
ƒ � a tensile, compressive, shearing, or bearing unit stress
A � cross-sectional area for tensile or compressive forces, or area on which
sliding may occur for shearing forces, or contact area for bearing loads
For torsional stresses, see Art. 5.4.2.
The unit strain for the axial tensile and compressive loads is given by the equation
where � � unit strain
e � total lengthening or shortening of the member
L � original length of the member
e
� � (5.22)
L
Applying Hooke’s law and Eq. (5.22) to Eq. (5.21) yield a convenient formula for
the deformation:
where P � load on the member
A � its cross-sectional area
E � modulus of elasticity of the material
PL
e � (5.23)
AE
[Since long compression members tend to buckle, Eqs. (5.21) to (5.23) are applicable
only to short members.]
While tension and compression strains represent a simple stretching or shortening
of a member, shearing strain represents a distortion due to a small rotation.
The load on the small rectangular portion of the member in Fig. 5.5 tends to distort
it into a parallelogram. The unit shearing strain is the change in the right angle,
measured in radians.
Modulus of rigidity, or shearing modulus of elasticity, is defined by
where G � modulus of rigidity
v � unit shearing stress
� � unit shearing strain
v
G � (5.24)
�
It is related to the modulus of elasticity in tension and compression E by the
equation
where � is a constant known as Poisson’s ratio.
E
G � (5.25)
2(1� �)