Chapter 7 Flashcards
What is torsion?
Twisting of a body segment when loaded by couples that produce rotation about its longitudinal axis.
What is the symbol and units for torque?
Symbol: T
Unit: Nm
What is the equation to calculate torque from force?
T = Fr
dT = dFr
T = Torque
F = Force
r = Radius of shaft
What is the symbol and unit for shear stress?
Symbol: τ
Unit: Nm^-2 or Pa
What is the equation for shear stress?
τ = F / A
dτ = dF/A
F = Force
A = Area
What is the symbol and unit for shear strain?
Symbol: γ
Unit: None
What is the equation to calculate shear strain?
γ = S/dx
S = Displacement of point on edge of shaft
dx = Length of shaft
What is the equation to calculate displacement of point on the edge of shaft?
S = rdθ
S = Displacement of point on edge of shaft
r = Radius
dθ = Change in the angle
What is the equation for rate of twist?
Rate of twist = dθ/dx
How can shear strain be calculated from rate of twist?
γ = rdθ/dx
What is the symbol and unit for shear modulus?
Symbol: G
Unit: Nm^-2 or Pa
What is the general equation for shear modulus?
G = τ/γ
What is the equation to calculate shear stress from rate of twist?
τ = Gγ
τ = Grdθ/dx
How can rate of change of torque be calculated from shear stress?
dT = τ dA r
dT = Rate of change of Torque
τ = Shear stress
dA = Change in area
r = Radius of shaft
How can torque of a CYLINDRICAL shaft be calculated from the second moment of area? What is the chain of equations?
T = ∫r τ dA
A = πr2
dA/dr = 2πr
dA = 2πr dr
T = ∫r τ 2πrdr
τ = Grdθ/dx
T = ∫r Grdθ/dx 2πrdr
T = G(dθ/dx) ∫2πr3 dr
What is the equation for the polar second moment of area for a cylindrical shaft?
J = ∫2πr^3 dr
J = (1/2)πr^4
What is the equation for torque of a shaft with regards to the second moment of area?
T = G(dθ/dx)J
What is the equation for torque with regards to power?
T = P/ω
T = P/2πn
T = Torque
ω = Revolutions per second
What is the torsion relationship?
T/J = Gθ/L = τ/r
What is the equation for torsion rigidity?
GJ = TL/θ
What is the equation for torsion stiffness?
GJ/L = T/θ
What is the equation for torsion flexibility?
L/GJ = θ/T
What is the equation that relates torsion stiffness and torsion flexibility?
Flexibility = 1/Stiffness
