Machinery's Handbook, 31st Edition
220
Combined Stresses Formulas for Combined Stresses (1) Circular Cantilever Beam in Direct Compression and Bending: Type of Beam and Loading Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
. d LF F 1273 8 d y x 2 − c
F
F y
0.5 a a τ ′ = σ ′
m
a b
σ = ′
a
F x
. d LF F 1273 8 d y x 2 + c
m
0.5 b τ ′ = σ ′ b
L
d
σ =− ′
b
(2) Circular Cantilever Beam in Direct Tension and Bending: Type of Beam and Loading Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
. d F d LF 1273 8 x 2 + c . d F d LF 1273 8 x 2 − c
a b
y
0.5 a τ ′ = σ′ a
m
σ = ′
F x F
a
F y
0.5 b b τ ′ = σ′
y
L
d
m
σ = ′
b
(3) Rectangular Cantilever Beam in Direct Compression and Bending: Type of Beam and Loading Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
bh h LF F 1 6 y x − c
F
m
F y a b
0.5 a τ ′ = σ′ a
a σ = ′
h
F x
bh h LF F 1 6 y x + c
m
σ =− ′
0.5 b τ ′ = σ ′ b
L
b
b
(4) Rectangular Cantilever Beam in Direct Tension and Bending: Type of Beam and Loading Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
bh F h LF 1 6 x + c bh F h LF 1 6 x − c
y
a b
m
σ = ′
= ′
0.5
τ
σ
F x F
′
a
a
a
h
F y
y
m
b σ = ′
0.5 b τ ′ = σ′ b
L
b
(5) Circular Beam or Shaft in Direct Compression and Bending: Type of Beam and Loading Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
. d LF F 1273 2 d y x 2 + c
F y a b
m
0.5 a a τ ′ = σ ′
σ =− ′
F x
F x
a
. d LF F 1273 2 d y 2 − c
L/2
m
b σ = ′
0.5 b τ ′ = σ ′ b
L
d
x
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