-Q3.50-. A cantilever beam as shown in the figure has a clear covering of 50 mm at the top and at the extension of the hook. The beam dimensions are b = 320 mm and d = 470 mm and reinforced with 3- 28 mmø at the top and a stirrup holder of 20 mmø at the bottom. The bars are confined by a 10 mmø stirrups spaced at 150 mm. f'c = 28.3 MPa and fy = 418.5 MPa. (1) Calculate the required development length or length of embedment (in at least 2 decimal places) for the straight top bars. Use Table 425.4.2.2., (2) Calculate the required development length or length of embedment (in at least 2 decimal places) for the top bars with a 90 degree hook and the length of straight extension. Provide sketch for the orientation of these dimensions., (3) Calculate the required development length or length of embedment (in at least 2 decimal places) for the top bars with a 180 degree hook and the length of straight extension. Provide sketch for the orientation of these dimensions. Table 425.4.2.2Development Length for Deformed Bars and Deformed Wires in TensioD20 mm o and smaller barsand deformed wiresSpacing and cover25 mm ¢ and larger barsClear spacing of bars or wires being developed or lap splicednot less than d,, ciear cover at least d,, and stirrups or tiesthroughout d, not less than the Code minimum,dy2.1A/f1.7A/T)orClear spacing of bars or wires being developed or lap splicedat least 2d, and clear cover at least d,dp1.1A/fe.Other casesdoTable 425.4.2.4425.4.2.3 For deformed bars or deformed wires, &a shal)be calculated by:Modification Factors for Development ofDeformed Bars and Deformed Wires in Tension11 fy w.YY,ModificationValue ofeConditlon(425.4.2.3a)factorfactor1.1 AF. (b+KırdpLightweight concrete0.75Lightweight concrete,where fet is specifiedInaccordanceLightweightin which the confinement term (C, + K)/d, shall notexceed 2.5, andwith Section 419.2.4.3Normal-weiglt concreteEpoxy-coated or zinc andcpoxy dual-coatedreinforcement with1.040AtrKtr(425.4.2.3b)1.5clcar cover Icss than 3d,or clear spacing less than6d,Epoxy-coated or zinc andepixy dual-coaledreinforceneot for allsnreinforcement location factorEpuxy"coating factorreinforcement size factorlightweight aggregate concrete factorsmaller of center of tension bar to nearest concrete surface or one- half center-1.2other conditionsCbUnconted or zinc-coatedto- center spacing of the barsKr(galvanized)rcinforcementtransverse reinforcement index1.01.025 mn o and Jarger bars20 mm o and smallerbars and deformed wiresSizeAtrtotal cross sectional area of transverse reinforcement having the center- to-0.8center spacing, s and a yield strengththe # of bars or wires being developed or lap spliced along the plane offס .תןות 300 Moretihansplitting. If steel is in two layers, n is the largest # of bars in a single layercenter- to- center spacing of transverse reinforcementCastingposition"fresh concrete placedbelow horizotal1,3SreinforcementOther1.0 clear coverLdhd.

Question

-Q3.50-. A cantilever beam as shown in the figure has a clear covering of 50 mm at the top and at the extension of the hook. The beam dimensions are b = 320 mm and d = 470 mm and reinforced with 3- 28 mmø at the top and a stirrup holder of 20 mmø at the bottom. The bars are confined by a 10 mmø stirrups spaced at 150 mm. f'c = 28.3 MPa and fy = 418.5 MPa. (1) Calculate the required development length or length of embedment (in at least 2 decimal places) for the straight top bars. Use Table 425.4.2.2., (2) Calculate the required development length or length of embedment (in at least 2 decimal places) for the top bars with a 90 degree hook and the length of straight extension. Provide sketch for the orientation of these dimensions., (3) Calculate the required development length or length of embedment (in at least 2 decimal places) for the top bars with a 180 degree hook and the length of straight extension. Provide sketch for the orientation of these dimensions. Table 425.4.2.2Development Length for Deformed Bars and Deformed Wires in TensioD20 mm o and smaller barsand deformed wiresSpacing and cover25 mm ¢ and larger barsClear spacing of bars or wires being developed or lap splicednot less than d,, ciear cover at least d,, and stirrups or tiesthroughout d, not less than the Code minimum,dy2.1A/f1.7A/T)orClear spacing of bars or wires being developed or lap splicedat least 2d, and clear cover at least d,dp1.1A/fe.Other casesdoTable 425.4.2.4425.4.2.3 For deformed bars or deformed wires, &a shal)be calculated by:Modification Factors for Development ofDeformed Bars and Deformed Wires in Tension11 fy w.YY,ModificationValue ofeConditlon(425.4.2.3a)factorfactor1.1 AF. (b+KırdpLightweight concrete0.75Lightweight concrete,where fet is specifiedInaccordanceLightweightin which the confinement term (C, + K)/d, shall notexceed 2.5, andwith Section 419.2.4.3Normal-weiglt concreteEpoxy-coated or zinc andcpoxy dual-coatedreinforcement with1.040AtrKtr(425.4.2.3b)1.5clcar cover Icss than 3d,or clear spacing less than6d,Epoxy-coated or zinc andepixy dual-coaledreinforceneot for allsnreinforcement location factorEpuxy&#34;coating factorreinforcement size factorlightweight aggregate concrete factorsmaller of center of tension bar to nearest concrete surface or one- half center-1.2other conditionsCbUnconted or zinc-coatedto- center spacing of the barsKr(galvanized)rcinforcementtransverse reinforcement index1.01.025 mn o and Jarger bars20 mm o and smallerbars and deformed wiresSizeAtrtotal cross sectional area of transverse reinforcement having the center- to-0.8center spacing, s and a yield strengththe # of bars or wires being developed or lap spliced along the plane offס .תןות 300 Moretihansplitting. If steel is in two layers, n is the largest # of bars in a single layercenter- to- center spacing of transverse reinforcementCastingposition&#34;fresh concrete placedbelow horizotal1,3SreinforcementOther1.0 clear coverLdhd.

Accepted Answer

Given that,
Clear cover=50 mm
b=320 mm
d=470 mm
Stirrup holder=20 mm
Stirrup space=150 mm
fc'=28.3…