Unformatted text preview: CIVL 232 Design of Structural Concrete
Assignment 2 (Tuesday, 2 March 2004)
Singly reinforced sections in bending, moment redistribution
2.1 (a) Describe the failure characteristics of an underreinforced beam and an overreinforced beam.
(b) Derive the formula for the design of a singly reinforced rectangular section in
bending:
M
As =
0.95 f y z ( where z = d 0.5 + 0.25 − K / 0.9
M
K= 2
bd f cu ) (c) Derive the condition to ensure yielding of tension steel at the ultimate limit state.
What value does BS 8110 limit the depth of neutral axis to?
2.2 A simply supported rectangular beam of 7.5 m span shown in Fig. 2.2 carries dead
(including selfweight) and imposed loads of 12 kN/m and 8 kN/m, respectively. The
beam dimensions are b x h = 250 x 500 mm. Calculate the area of reinforcement
required. fcu = 30 N/mm2, fy = 460 N/mm2 , d = (h – 50) mm. 500 Gk = 12kN/m, Qk= 8kN/m As 7500 250 Fig. 2.2
2.3 A reinforced concrete beam of 300 mm wide and 600 mm deep is required to span 6
m, as shown in Fig. 2.3. The beam carries dead and loads of 25 kN/m and 19 kN/m,
respectively. Design the beam section for bending. fcu = 30 N/mm2, fy = 460 N/mm2. 600 Gk = 25kN/m, Qk= 19kN/m As 6000 300 Fig. 2.3 2.4 The crosssection of a RC beam shown in Fig. 2.4 carries a design ultimate moment
M = 160 kNm. Determine the area of reinforcement required. fcu = 25 N/mm2, fy =
460 N/mm2.
100 100 400 80 1 00 As
300 Fig. 2.4
2.5 Determine the theoretical value of the concentrate load P that will cause the underreinforced beam in Fig. 2.5 to fail in flexure. fcu = 30 N/mm2, fy = 460 N/mm2. 400 P 2m As 2m 250
A s = 9 42mm 2 ( 3T20) Fig. 2.5
2.6 A simply supported RC beam with fcu = 30 N/mm2, fy = 460 N/mm2 contains 1960
mm2 of tension reinforcement (Fig. 2.6). If the span is 7m, determine the maximum
imposed load that the beam can carry. Assume that the load is: (a) an uniformly
distributed load, and (b) a point load at midspan.
200 200 300 Fig. 2.6 As 200 4T25 700 5 00 200 600 Fig. 2.7 2.7 Calculate the moment of resistance for the crosssection shown in Fig. 2.7. fcu = 30
N/mm2, fy = 460 N/mm2, As = 1963 mm2 (4T25). 2.8 Answer the following the questions:
(a) Why do we consider the moment redistribution in design of a RC continuous
beam (an indeterminate structure)?
(b) What are the maximum moment redistribution permitted in BS 8110 and its
corresponding moment redistribution ratio?
2.9 The beam shown in Fig. 2.9 is subjected to an increasing uniformly distributed load.
It is assumed that the ultimate bending strength at supports is 70% that at the midspan and equal to wL2/12, where w is the UDL to cause the first plastic hinge.
Determine:
(a) the collapse load that the beam may carry with moment redistribution.
(b) the moment redistribution ratio at section C. Fig. 2.9 ...
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This note was uploaded on 12/24/2011 for the course CIVL 232 taught by Professor Jskuang during the Spring '06 term at HKUST.
 Spring '06
 JSKUANG

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