AAiT, School of Civil and Environmental Engineering

Transcription

1 Example 1 of Example.9: An interior T beam in a floor system has a center to center span of 5.5 m and cross section shown in the figure. The concrete and steel grades are C0/5 and S400 respectively. Compute the design resistance capacity of this beam in the positive moment region. (Cover to stirrup = 5 mm and stirrup of diameter 8 c/c 00 was provided) Step 1: Design Values ( Changing the characteristic value to design value) d 500 (5 8 10) 457 mm Formula 3.15 for persistent and transient design situation: NB: Take Table.1N Section British National Annex Examples on analysis of flanged reinforced sections Page 1

2 Step : Determine the effective flange width of the beam Example 1 of section The effective flange width b eff for a T beam or L beam may be derived as: where and b eff, i b i b b b b eff eff, i w b 0.b 0.1l 0.l eff, i i For the given beam, b m and b m Since the beam is an interior beam and the design moment resistance is required to be estimated for the positive moment region, l 0.7l 0.7 * m 0 Thus, b 0.b 0.1l 0. * * m eff,1 1 0 b 0.b 0.1l 0. * * m eff, 0 Step 3: beff b1 b bw m Assume the neutral axis to be in the flange Examples on analysis of flanged reinforced sections Page

3 Step 4: Assume the strain the tension reinforcement to be greater than the yield strain Step 5: Use the procedure of analysis of singly reinforced concrete sections to estimate neutral axis depth Example 1 of Step 6: Step 7: c Using the general design chart, kx 0.09, x Check if the assumption in step 3 is correct x , the assumption is correct! Calculate the moment resistance Using the general design chart, s1 5, the assumption is correct! k 0.987, z z M Asf ydz 4 * *10 * * kNm Examples on analysis of flanged reinforced sections Page 3

4 Example of Example.10: Compute the design resistance of the T beam shown in the figure below. The concrete and steel grades are C0/5 and S460 respectively. (Cover to stirrup = 5 mm and stirrup of diameter 8 c/c 00 was provided) Step 1: Design Values ( Changing the characteristic value to design value) d 700 (5 8 1) 655 mm Formula 3.15 for persistent and transient design situation: NB: Take Table.1N Section British National Annex Step : Step 3: Step 4: Assume the neutral axis to be in the flange Assume the strain the tension reinforcement to be greater than the yield strain Use the procedure of analysis of singly reinforced concrete sections to estimate neutral axis depth Examples on analysis of flanged reinforced sections Page 4

5 Step 5: c Using the general design chart, kx 0., x Check if the assumption in step 3 is correct x , the assumption is not correct! Example of Step 6: Take the neutral axis to be below the flange and divide the section into two parts: Beam W and Beam F to simplify the analysis process. Step 7: Take the rectangular stress strain relationship for the concrete under compression and calculate the moment resistance using force equilibrium. Beam F A sf fcd be bw hf * * mm f 400 yd ( ) or ( ) MRd, f * *15 * kNm The force in the remaining steel area A sw is balanced by compression in the rectangular portion of the beam. (i.e. A sw = A s - A sf ) Beam W A A A 4 * * mm sw s sf Examples on analysis of flanged reinforced sections Page 5

6 Example of 94.4 * 400 x mm 0.8 *11.33 * 50 or MRd, w * 50 * 0.8 * * * knm The total moment capacity of the section now becomes, MRd knm Step 8: Calculate the strain in the tension reinforcement and check if the assumption is step is correct. If it s not found to be true, revise the procedure assuming the steel has not yielded. x d d 3.5 * 655 s x s yd..ok! Examples on analysis of flanged reinforced sections Page 6