Machinery's Handbook, 31st Edition
Combined Stresses
221
(6) Circular Beam or Shaft 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 2 x 2 − c . d F d LF 1273 2 x 2 + c
F y a b
y
0.5 a τ ′ = σ′ a
m
a σ = ′
F x
F x
L/2
y
m
d
L
0.5 b τ ′ = σ ′ b
b σ = ′
(7) Rectangular Beam or Shaft 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 2 3 y x + c
F y a b
m
0.5 a τ ′ = σ ′ a
F x
σ = − ′
F x
a
h
L/2
3
LF F y
1
σ = − ′ c
m
0.5 b τ ′ = σ ′ b
−
b
L
bh h 2
x
b
(8) Rectangular Beam or Shaft 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 2 3 x − c
F y a b
y
m
F x
a σ = ′
0.5 a τ ′ = σ ′ a
F x
h
L/2
bh F h LF 1 2 3 x + c
y
m
σ = ′
0.5 b τ ′ = σ ′ b
b
L
b
(9) Circular Shaft in Direct Compression and Torsion: Type of Beam and Loading Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
d T T F a a anywhere on surface F
. d F d T 0637 8 2 2 + a
. d F F d T 0637 8 2 2 ± + a ;
2
2
′
k
k
E
a τ =− ′
σ =−
a
(10) Circular Shaft in Direct Tension and Torsion: Type of Beam and Loading
Maximum Nominal Tensile or Compressive Stress
Maximum Nominal Shear Stress
d T T F a a anywhere on surface F
′
′
τ
σ
=
=
. d F d T 0637 8 a 2 2 + a
. d F F d T 0637 8 a 2 2 ± + a ;
2
2
k
k
E
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