Bending

Question 1

Beam Assumptions

Answer 1

• Length is much bigger than its width
• Initially straight
• Constant cross-section
• Uniform material

Question 2

What is the centroid of a beam?

Answer 2

Cross-section on the neutral plane.

Question 3

What is direct stress?

Answer 3

Internal reaction of a beam due to bending.

Question 4

Hookes Law for beams

Answer 4

σ[z] = -E*(y/R)

Question 5

Flexure Formula

Answer 5

σ[z] = (M*y)/I

Achieved at furthest away point from centroid on the neutral axis. y = this distance.

Question 6

Parallel Axis Theorem (PAT)

Answer 6

Allows to find I of difficult cross sections.
Split section into 3 parts (top+bottom flange & web)

Question 7

How to calculate PAT

Answer 7

1) Locate datum
2) Find local centroid of sections
3) Find centroid of entire cross-section
4) Find co-ordinates of local sections

I[xx] = Ixx + b²A

Question 8

Deflection of Beams due to Bending Equation

Answer 8

δ = P(Le)³/48EI

Question 9

Bending Moment Distribution in a Cantilever

Answer 9

M = Wl - Wx

Question 10

Bending Moment Distribution in a Simply supported beam

Answer 10

Left of Force:
M = -(W/2)*x

Right of right:
M = (W/2)*(z - l)

Question 11

Bending Moment Distribution in a UDL Cantilever

Answer 11

(W/2)*(l - z)²