Crosssectional Area

The cross-sectional area of a composite shape can be expressed as:

where:

Atotai is the total area of the composite cross-section Ai is the cross-sectional area of each component part

Consider the composite shapes indicated in (i) to (ix) and determine the value of Atotal

Figure 2.9
Figure 2.10

Figure 2.11

Ami [(LOO x 10) + {150 x S) + (100 x 10}] 3200 turn1

Figure 2.12

Figure 2.13

_ ¿-A f(O.S * 30 x 50) + (70 y 50) + (0.5 x 50 X 50)1 ~ 5500 mnr Note: for it trapezium in general;

I I x

Figure 2.15

1=1 K {lie sum uflKc Irn^lhs uflhc parjlkl sides) K (perpend iculur huijjlitH

Check the area of the trapezium in (vi): Atotal=[0.5x(70+150)x(50)]=5500 mm2 In a similar manner to adding the individual areas of component parts to obtain the total area, section properties can be evaluated by subtracting areas which do not exist, e.g. in hollow sections. Consider examples (vii) to (ix).

Figure 2.16

Figure 2.17

Figure 2.18

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