Parallel axis theorem & introduction to shear stresses

Question 1

What happens when a beam bends?

Answer 1

When bending a beam the top fibers become short and are in compression and the bottom fibers become longer and are in tension

Question 2

How can the bending stress be calculated?

Answer 2

σ = My/I

Question 3

What is the allowable stress?

Answer 3

Allowable stress being the maximum stress that can safely applied to a structure

Question 4

How can you find longitudinal strain from the radius of curvature?

Answer 4

y/R
y - distance below the neutral axis

Question 5

How can stress be calculated from the radius of curvature?

Answer 5

σ = Eε_x = Ey/R

Question 6

What happens when a beam is bent about the z-axis?

Answer 6

Deforms into a circular arc

Question 7

How does stress change with distance y from the neutral axis?

Answer 7

Stress varies linearly with distance y

Question 8

What does the second moment of area describe?

Answer 8

I describe the flexural stiffness of the member

Question 9

What does a higher I mean?

Answer 9

Section with larger I is harder to bend and is able to carry a higher moment

Question 10

What is the I for rectangular beam?

Answer 10

I = bh^3/12

Question 11

What is the formula for the parallel axis theorem?

Answer 11

I_BB = I_AA + Ah^2

Question 12

What is the value of the first-moment area about the neutral axis?

Answer 12

The first moment of area about the neutral axis is zero so cancels out

Question 13

How can you determine the elastic section modulus?

Answer 13

Z = I/y_max

Question 13

What does a beam subject to bending experience?

Answer 13

Beam subject to bending experiences a moment and a shear force i.e., shear stress

Question 13

What is it called when shear stress exists in pairs?

Answer 13

Complementary shear stresses

Question 14

How can equilibrium in a structure be maintained?

Answer 14

The shear forces are in the opposite direction but same magnitude to maintain equilibrium

Question 15

What is the effect of shear?

Answer 15

The effect of shear is to initially deform the element for example from square to parallelogram

Question 16

How can rotational equilibrium be maintained?

Answer 16

Need horizontal component of shear stress

Question 17

What are diagonal tension cracks?

Answer 17

Develop in the beam when the strength of the beam in diagonal tension is less than the strength in flexural tension.

Question 18

What is transverse shear also known as?

Answer 18

Horizontal shear

Question 19

What can demonstrate the existence of horizontal stresses?

Answer 19

When planks are bonded together and a load is applied, there is no relative sliding and therefore there is a horizontal stress

Question 20

How do shear stresses act?

Answer 20

Shear stresses are parallel to the plane on which they act

Question 21

How do axial stresses and bending act?

Answer 21

Axial and bending are perp. to the plane

Question 22

How can shear stress be found?

Answer 22

𝜏 = VQ/Ib = VAy/Ib

Question 23

What is shear force directly proportional to?

Answer 23

Magnitude of stress

Question 24

What is stress at outer most fiber?

Answer 24

0

Question 25

When is shear stress the largest?

Answer 25

At the neutral axis

Question 26

How does shear stress vary?

Answer 26

Shear stress varies in a parabolic fashion from zero to a max value at the neutral axis