1) Frame Design Equations

Question 1

What are the strain equations for Tension, Torsion and Bending?

Answer 1

Tension: Strain = change in length/ original length

Torsion: Angular Distortion = radius * angle / length

Beam: Strain = radius of beam / radius of bend

Question 2

What are the stress equations for tension, torsion and bending?

Answer 2

Tension:
Stress = youngs modulus * strain

Torsion:
Stress = shear modulus * angular distortion

Bending:
Stress = youngs modulus * strain

Question 3

What are the equilibirum equations for tension, torsion and bending?

Answer 3

Tension:
Stress = load/Area

Torsion:
Stress = torque * radius / J

Bending:

Stress = Moment * radius / I

Question 4

How do you calculate G from E and v?

Answer 4

G = E / 2(1+v)

Question 5

What is the formula for I? Give for hollow and solid beams.

Answer 5

I (solid) = pi * D^4 / 64

I (hollow) = pi * (D-d)^4 / 64

Question 6

What is the formula for J?

Answer 6

J = 2*I

Question 7

Whats the formula for A for solid and hollow beams?

Answer 7

A (solid) = pi * r^2
A (hollow) = pi * (r1^2 - r2^2)

Question 8

What is the moment of failure formula?

Answer 8

M failure = yield stress * r^2 * t

Question 9

What is the critical moment formula?

Answer 9

M critical = E * r * t^2

Question 10

What is the stiffness equation?

Answer 10

E * I

I = pi * r^3 * t

Question 11

What is the formula for area of a hollow tube?

Answer 11

2 Pi * r * t