For practical purposes the rectangular stress block used for the design of beams (see Chapter 4, originally published as Beams9) may also be used for the design of columns (see Figure 7). However, the maximum compressive strain for concrete classes up to and including C50/60, when the whole section is in pure compression, is 0.00175 (see Figure 8a). When the neutral axis falls outside the section (Figure 8b), the maximum allowable strain is assumed to lie between 0.00175 and 0.0035, and may be obtained by drawing a line from the point of zero strain through the 'hinge point' of 0.00175 strain at mid-depth of the section. When the neutral axis lies within the section depth then the maximum compressive strain is 0.0035 (see Figure 8c).
Strain diagrams for columns
0.0035 max s
a) Pure compression b) When x > h c) When x < h d) General relationship d h h e s x
The general relationship is shown in Figure 8d). For concrete classes above C50/60 the principles are the same but the maximum strain values vary.
Two expressions can be derived for the area of steel required, (based on a rectangular stress block, see Figure 7) one for the axial loads and the other for the moments:
AsN = Area of reinforcement required to resist axial load NEd = Axial load fcd = Design value of concrete compressive strength asc (ast) = Stress in compression (and tension) reinforcement b = Breadth of section dc = Effective depth of concrete in compression = Lx < h L = 0.8 for < C50/60 x = Depth to neutral axis h = Height of section
Asm/2 = [M - fcd b dc(h/2 - dc/2)] / [(h/2^) (asc+ast)] where
AsM = Total area of reinforcement required to resist moment
Realistically, these can only be solved iteratively and therefore either computer software (e.g. RC Spreadsheet TCC53 from Spreadsheets for concrete design to BS 8110 and EC27) or column design charts (see Figures 9a to 9e) may be used.
Column design chart for rectangular columns d2 /h = 0.05
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