Question

Fig. Q-1 shows a two-span continuous beam which is to carry a characteristic dead load inclusive of self-weight, gk, of 12 kN/m, and a characteristic imposed load, qk, of 10 kN/m. Material properties are: fek = 25 MPa, and fyk = 500 MPa. (a) Determine the design bending moment envelope for span AB. You need not have to consider moment re-distribution. [10 marks] (b) Determine the maximum moment that the support section at B can carry if the neutral axis depth, x, at ultimate limit state, is to be limited to 0.4d, where d is the effective depth of the tensile reinforcement. Hence, calculate the required reinforcement for the support section at B to resist the design bending moment obtained in (a). Assume an axis distance of 50 mm to all longitudinal bars. [15 marks] 800 6 > 1001 400 ABAC l 6m > 4m All dimensions are in mm. Fig. 2-1

Answer 1

Answer From the given data : . -Dead road inclusive of sel weight gk 10. characterstic imposed load qk = 24KNITT , - tekiz 3099 Pa.,,.. ' - Syk = 500MPO.. aj let us determine design bending moment for mið spas section of AB. Coknim w. pen. unit length - Kem x 8m w is taken as = Dead load + Impored load in : 20+ 24 = 44k nim - Design Bending moment at a midspan of continous Peaned with opamne AB is given as we?

But we have to consider support moments as it is a contingum Beam - we are using moment disturbution method to calculate support moment Stepe Distribution jactor 2:05 Kga - yes Difbo be on Re KBC=YET EK: BEI DF BOEKBC = -0.5 Fiaet end moment's * * . -W2² consider both spon supports Jiaed P11688 = - We? Pirge - We MFBA - we? MFCB = we? Step3 ;- - sian convention thout the Hoga-ve. B LC Initial FOM As support' Áre' are pimmed support, we release the moments by balancing it applying equal opposite i moment. 1 Y carrying over moment wires it takten half of the Balon crop "'", carry i y . but - over moment' - - final o out - opet o! FEN CS$canned with CamScanner

Stepy. MFAB=0 Mfgc = -We? .. MFBA: We prog: weed As 8 support is alio pinned the moment is balanced at o support... ! . . . steps. Bno diagram s Design moment P o moment diagona 19id spon moments we = 44x8?352 kNm support moment o cota +352 kWm' so design moment at mid span. = 0042 - The Jaz [support moment hajat mildapon] = 852- (176) • 146k NM Design moment of mid spon = 156kNm Of A B Spon 2) me 146kNm - considering daetor alls :,:. :inquo. 2648NM för fe sood - Humax =0.46 .. ii. ... d: 600. cover 600-60 = 540i , . Xumax = 0.46% 540 = 248.4 CS$canned with CamScanner

...SO NA lies in web for Balanced section ci) of $0.2 or PL 70.yg guse all , =t00mm do 540 mm, 60.:300mm blasoomm 100 -0.18 $0.2 or 100 70.49 Tuse of XUmese 540 .......2484 Molim = cxz = ?170232 - Given je 2s, code = 0.86 pek bw ocu'max[d; 0.42 gcuniax] +0.446 Jek (boy-bwj ej Ca- og = '0.86 x 30 x 300:248-4 [540-0.42.248.47. : +0.4468 30x (800-300). 500[540-100) : 350.63+324.81 = 678.44 kw.m ATUL Mulim - so design as under reinforced section- 90 MUR = 190 XU = xumax Mol= TX2 .=0.874 A8+ [d-a] . a= cry, tczyz ... cite -,9:36j ek bw xu máx Ta=0.42 XUNQxJ :. 70.446 jck (l-bw) old-RET 0.36ick box.umax +0.446 fok (bj bw) & DI 350.63+327-81 X10 678:44 xr06 8048167 66900 1 443816 54601328 mm CSscanned with CamScanner .: 0:9 A y . .... . .. ... .

Molim : 0.84 x 500. Ast (540-460-315 0.89 x 500 YA ST [198427 264 X106: 34654:32 RASTE Ast=7614.43 mm2 considering 82mm diameter Area of single bara T *32?= 804.24 mm2 30. no. of Steinforcements 4614:43 804-24 -9.44 bars so keep asf so provide a bars of 32 mm in two layer of 4.5 in each layer. ,."..... 3) limit state of deflection *factual) + (Permissible.... à (actual) = 8000 =14.81 → (Permissible) -26 sponsrom continus beam=y 5:26 Flactwa ) = 14.81 18 code 456-2000 table til. 540 + ( Parmi leible) =26. L so it deplection is not greater than the permissible so the eriteria is eatisfied summary Derian moment = 864.Nm Reinjorcing bars 8 bars of 82mm in-two layers. Reinforcing a 800m 100mm OOO bodrom .8 bars 32mmd in two layers Klooming - CS Scanned with CamScanner

e ) Saje in criteria al deplection as serviçea biting Criteria (actual= 14 + < ( Permissible) = 26 . csscanned with CamScannei +