Moment diagrams by Superposition

CIV2503 Structural Design I 1

CIV2503 Structural Design I

Dr Yan Zhuge

University of Southern Queensland

Email: zhuge@usq.edu.au

Superposition

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Most loadings on the

beam will be a

combination of the

loadings shown in Fig

4.20

If we use the method of

superposition, each of

the loads can be treated

separately and the

moment diagram be

constructed in a series

of parts.

Superposition

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To understand the

method of

superposition to

construct moment

diagram, consider

the simply

supported beam in

Fig 4.21(a)

Superposition

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The reactions have been calculated

The moment diagram for this case is shown at the top

of Fig 4.21(b)

Rather considering all the loads on this beam

simultaneously when drawing the M diagram, we can

instead superimpose the results of the loads acting

separately on the three cantilevered beams shown in Fig

4.21(a)

Superposition

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For e.g., from each of the separate moment

diagram, M at end A = -500-750+1250 = 0

This is verified by the top moment in Fig 4.21(b)

In a similar manner, we can also simplify

construction of the resultant moment

diagram for a beam by using a superposition of

simply supported beams

Superposition

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For e.g., the loading on the beam shown

at the top of Fig 4.22(a) is equivalent to

the beam loadings shown below it

Separate M diagrams for each of the 3

beams can be used rather than drawing

the resultant moment diagram shown in

Fig 4.22(b)

Example 1

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Example 2

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Draw the M diagram for the beam shown,

using the method of superposition

Consider the beam to be cantilevered

from the support at B.

Example 2

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If the beam were to

be supported as a

cantilever, it would be

subjected to the

statically equivalent

loading shown in Fig

4.23(a)

Example 2

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The superimposed 3

cantilevered beams

are shown together

with their associated

M diagrams in Fig

4.23(b)

The sum of these

diagrams will yield

the resultant

moment diagram for

the beam