7. Beams, stress due to bending

Question 1

What are the assumptions made in engineers bending theory?

Answer 1

Question 2

What is the neutral surface and neutral axis?

Answer 2

Question 3

What is the equation for longitudinal strain, in a bending beam?

Answer 3

Question 4

What are the equations for Poisson’s ratio in a bending beam?

Answer 4

Question 5

What is the equation for longitudinal stress distribution for a bending beam?

Hint: uses hooke’s law and longitudinal strain for bending

Answer 5

Note:
* Stress varies linearly with y (distance from netural axis).
* Maximum values are on the external surfaces. (the netural axis is considered 0, so above surface = negative values, lower surface = positive values).

Question 6

What is the equation for first moment of area? How do you work out the netural axis position from this equation?

Answer 6

Question 7

What is the equation for second moment of area?

Answer 7

Question 8

What is the equation known as engineer’s bending theory? What is an assumption made in the theory?

There is technically two ways to often depict this. Either is fine.

Answer 8

Question 9

How would you evaluate the strength of a beam with uniform cross section, using engineers bending theory?

List steps.

Answer 9

Question 10

How does superposition work to work out the internal longitudinal stress distribution?

Answer 10

• You take the bending stress and the axial stress and combine to get the final stress distribution.
• Only works for linear elastic materials.