Mechanics of beams

Question 1

How many reactions can a Roller support provide?

Answer 1

One: reaction normal to the surface.

Question 2

How many reactions can a Pin or Hinge support provide?

Answer 2

Two: can support vertivcal and hortizontal loads.

Question 3

What are the 5 steps when finding the reactions at the supports of a truss?

Answer 3

1. Draw a free body diagram showing both hortizontal and vertical components of any angled forces.
2. Place and label the unknown forces at the supports (choose a direction for each)
3. Take moments around the non-roller support to determine the reaction at the roller support.

ΣM = 0 (clockwise is positive)

4. Find reaction at pin support by ΣF_v=0 and ΣF_H=0
5. Find the totla reaction by adding (pythagoras) both vectors.

Question 4

What are the two methods for analysing the forces inside a beam of a Truss?

Answer 4

1. Method of joints
2. Method of sections

Question 5

1. Using the method of joints: find the force in members AF and EF.

Answer 5

Question 6

2. Using method of sections determine the force in the members.

Answer 6

Using ΣM=0, ΣF_v=0, ΣFH=0 solve fopr the forces. Hint try to use an equation that takes out two of the unknown forces.

Question 7

What is the difference between a shear force and a bending force.

Answer 7

Question 8

What is the method for drawing a shear force diagram?

Answer 8

1. Draw a freebody digram showing all known loads (calculate the reactions at the supports and watch for the weight of the beam).

2. Draw your SF directly below your freebody diagram.

3. Start at left sideand plot up for upward forces and down for downward forces.

4. Your diagram should be balanced ie end at zero

Question 9

What is the method for drawing a bending moment diagram.

Answer 9

1. Draw your BM diagram directly below your SF diagram.
2. Bending moments are always zero at the ends of a beam (except a cantilever beam).
3. Calculate moments by determining the areas of the SF diagram.
4. Positive areas give positive gradients, negative areas give negative gradients.
5. Useful check: at positions of zero SF BM is at a maximum.

Question 10

How does a Cantilever beam effect SF and BM diagrams

Answer 10

1. Draw in the reaction at the wall (sum of two downward forces)
2. Draw in SF diagram as usual
3. Calculate the bending moment at the wall (this will always be negative for a cantilever and plot this point on the y-axis.

Question 11

When a beam is subjected to bending, not all of the beam undergoes the same type of stress. What happens to the beam?

Answer 11

The top surface undergoes compression

The bottom surface undergoes tension (not good for concrete)

A neurtal axis is formed.

Question 12

What do the variables in the following formula stand for?

and what are the units?

Answer 12

Question 13

On your formula sheet the bending stress formula is given to you in what form?

Can one beam have different Y values

Answer 13

Yes- if the beam is not symmetrical you can have different distance form the neutral axis and the top and bottom surfaces.

Question 14

Some tips when using the Bending Stress formula

Answer 14

1. write down the formula
2. Bending moment (M) can be found from the maxmium bending moment on your BM diagram.
3. Check your units, everthing needs to be in metres and newtons etc.
4. mm to m ( x10^-3 )