BCGBC4010A Apply structural principles to residential low-rise constructions

Structural principles - Structural members

Beams

Bending moments
Match the following sentences with the appropriate graph.
Sentences
1.	Simple beam central point load. There is a diagram of a beam of length L with load P applied downwards onto the middle of the beam. Arrows indicating supports are shown at each end of the beam, pointing upwards.
A graph beside this is shown as an example. The graph shows an isosceles triangle. The bottom left corner of the triangle has the label BM=0. The top of the triangle has the label BMmax = PL/4.
2.	Simple beam UDL. There is a diagram of a beam of length L with UDL = W shown. This is represented as a force applied all along the length of the beam. Arrows indicating supports are shown at each end of the beam, pointing upwards.
3.	Simple beam off-set point load. There is a diagram of a beam of length L. 
A point load P is applied at a length a from one end of the beam and b from the other end. Arrows indicating supports are shown at each end of the beam, pointing upwards.
4.	Cantilever beam point load. There is a diagram of a beam of length L attached to a support member. A load P is applied downwards at the non-supported end of the beam.
5.	Cantilever UDL. There is a diagram of a beam of length L attached to a support member. A load UDL = W is applied along the length of the beam.
Graphs
A.	A diagram of a shape that is almost like a right-angled triangle except that the longest side is curved inwards. The right angle is at the top left corner. The right angle has the label BM = 0, and the lowest point has the label 
BMmax = - WL/Z.
B.	A diagram of a semicircle with the base at the bottom. The lowest point is labelled BM = 0 and the highest point BMmax = WL/8.

C.	A diagram of a triangle with uneven sides. The longest side of the triangle is at the bottom. The lowest point of the triangle is labelled BM = 0 and the highest point is labeled BMmax = Pab/L.
D.	A diagram of a right angled triangle with the right angle in the top left of the diagram. The highest point of the triangle is labelled BM = 0 and the lowest point is labelled BMmax = - PL.
Answers
1.	Simple beam UDL matches diagram D.
2.	Simple beam off-set point load matches diagram B.
3.	Cantilever beam point load matches diagram C.
4.	Cantilever UDL matches diagram A.
The graphs show the formulas which are used to determine the maximum bending moment BMmax.
Note the convention of using positive values for BMmax above the baseline (where BM = 0) and negative values for BMmax below this line.
If you are unsure about any of these graphs and would like to know more, talk to your trainer.

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