Performance Index

Question 1

What is the stress felt on a beam in 3 and 4 point loading?

Answer 1

3 -σ = 3FL/2bh^2
4 - σ = 3F(L-L1)/2bh^2
F = force applied, L = length between bottom points, L1 = length between top points, b = width, h = height

Question 2

What is the moment of inertia for a cantilever beam?

Answer 2

I = bh^3/12
I = inertia, b = width, h = height

Question 3

What is the second moment of area of a uniform wire? And of a tube

Answer 3

Ix = Iy = 0.25.πr^4
Tube - 0.25π(r2^4 - r1^4)
r1 = inner radius, r2 = outer radius

Question 4

Define the second moment of area

Answer 4

Efficiency of a cross sectional shape to resist bending

Ix=Iy for uniform shapes

Question 5

Define stiffness

Answer 5

Force/deflection

Question 6

Define torsional stiffness

Answer 6

GI/Lo

Shear modulus.inertia/ angular displacement

Question 7

Relationship between shear modulus and Young’s modulus?

Answer 7

G = E/(1-poisons ratio)

Question 8

Define longitudinal stress

Answer 8

σl = P.cap area/cross area
= Pr/2t
Pressure.radius/2xthickness

Question 9

Define hoop stress

Answer 9

σh = P.plane area/ material area
= Pr/t
Pressure.radius/thickness