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Unformatted text preview: CIVL 232 Design of Structural Concrete
Assignment 3 (Tuesday, 9 March 2004)
Doubly reinforced and flanged sections in bending
1. (a) Derive the equation for the condition to ensure yielding of the compression steel
at the ultimate limit state.
(b) Derive the design formulae for doubly reinforced rectangular sections in bending
in BS 8110:
( K − K ′) f cu bd 2
K ′f cu bd 2
As′ =
+ As′
and As =
0.95 f y ( d − d ′)
0.95 f y z
where
z = d (0.5 + 0.25 − K ′ / 0.9 ) , K ′ = 0.402( β b − 0.4) − 0.18( β b − 0.4) 2 , K = M / f cu bd 2 (c) Derive the design formulae for flanged sections with compression reinforcement
where 030% moment redistribution can be applied. [Eqs (2.62) for A’s and (2.63) for
As are only used in the case where moment redistribution is not larger than 10%] d'=50 2. The section shown in Fig. 32 is to resist an ultimate design moment of 330 kNm.
Determine the areas of reinforcement required. f cu = 30 N/mm 2 , f y = 460 N/mm 2 . h=550 As' As 250 Fig. 32
Determine the ultimate moment of resistance of the crosssection shown in Fig. 33.
f cu = 30 N/mm 2 , f y = 460 N/mm 2 . (a) As = 2454 mm2 and As′ = 942 mm2; and (b)
d'=50 As = 2454 mm2 and As′ = 1472 mm2. As'
d=500 3. As 300 Fig. 33 The Tsection beam shown in Fig. 34 is required to resist a design ultimate moment
of 180 kNm. Calculate the area of reinforcement required, (a) without, and (b) with
the assumption x = 0.5d (the code method). f cu = 30 N/mm 2 , f y = 460 N/mm 2 . d=350 hf=100 4. 100 200
400 100 Fig. 34
5. If the section in Fig. 34 is required to resist a design ultimate moment of 220 kNm,
design the section. d=500 hf=100 6. Determine the ultimate moment of resistance of the T section shown in Fig. 36. (a)
As = 4700 mm2; and (b) As = 5500 mm2. b = 1100 mm, bw = 350 mm, hf = 100 mm, d
= 500 mm; fcu = 30 N/mm2 and fy = 460 N/mm2 As bw=350 375 375 b=1100 Fig. 36 600
900 70 70
130 130
900 (a) Fig. 37 75 75 2T25 2T25 600 360 100 150 7. Determine the ultimate moment of resistance of the crosssections shown in Fig. 37.
(a) fcu = 25 N/mm2 and fy = 460 N/mm2; (b) fcu = 30 N/mm2 and fy = 460 N/mm2. 8T25
150 350
650 (b) 150 ...
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 Spring '06
 JSKUANG

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