fundamentals of engineering supplied-reference handbook - Ventech!

UNIAXIAL STRESS-STRAIN
Stress-Strain Curve for Mild Steel
♦
The slope of the linear portion of the curve equals the
modulus of elasticity.
DEFINITIONS
Engineering Strain
ε = ∆L / L0, where
ε = engineering strain (units per unit),
∆L = change in length (units) of member,
L0 = original length (units) of member.
Percent Elongation
⎛ ∆L
⎞
% Elongation = ⎜ × 100
⎝ L ⎟
⎠
o
Percent Reduction in Area (RA)
The % reduction in area from initial area, Ai, to final area,
Af, is:
⎛ Ai − Af
⎞
%RA = ⎜ × 100
⎝ A
⎟
⎠
True Stress is load divided by actual cross-sectional area.
Shear Stress-Strain
γ = τ/G, where
γ = shear strain,
τ = shear stress, and
i
G = shear modulus (constant in linear force-deformation
relationship).
E
G = , where
2 1
( + ν)
E = modulus of elasticity
v = Poisson's ratio, and
= – (lateral strain)/(longitudinal strain).
MECHANICS OF MATERIALS
38
Uniaxial Loading and Deformation
σ = P/A, where
σ = stress on the cross section,
P = loading, and
A = cross-sectional area.
ε = δ/L, where
δ = elastic longitudinal deformation and
L = length of member.
E
δ =
= σ ε =
PL
AE
P
δ
A
L
THERMAL DEFORMATIONS
δt = αL (Τ – Τo), where
δt = deformation caused by a change in temperature,
α = temperature coefficient of expansion,
L = length of member,
Τ = final temperature, and
Τo = initial temperature.
CYLINDRICAL PRESSURE VESSEL
Cylindrical Pressure Vessel
For internal pressure only, the stresses at the inside wall are:
2
o
2
o
2
i
2
i
r + r
σt = Pi and 0 > σr
> −Pi
r − r
For external pressure only, the stresses at the outside wall
are:
2
o
2
o
2
i
2
i
r + r
σt = −Po
and 0 > σr
> −Po
, where
r − r
σt = tangential (hoop) stress,
σr = radial stress,
Pi = internal pressure,
Po = external pressure,
ri = inside radius, and
ro = outside radius.
For vessels with end caps, the axial stress is:
σ
a
= Pi
r
2
ri
2 2
o − ri
These are principal stresses.
♦ Flinn, Richard A. & Paul K. Trojan, Engineering Materials & Their Applications,
4th ed., Houghton Mifflin Co., 1990.