Design of Shear Key
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xxx DESIGN OF SHEAR-KEY BELOW COLUMN BASE-PLATE Actual longitudinal shear force = 300 kN L/C : Actual transverse shear force = 93 kN node : Grade of concrete = 30 MPa Crushing strength (per BS 5950, Cl. 4.13.2.1) = 0.6 x 30 MPa = 18 Shear strength (per ACI-318) = 4 x 0.85 x ( 30 x 145.038 x 0.8 ) ^ 0.5 ps = 200.6 psi = 1.38 0.85 (Concrete characteristic cube strength converted to cylinder strength by multiplying with a factor of 0.8) Shear Key Section : Member = UC203x203x46 D = 203.2 mm B = 203.6 mm 11 mm 7.2 mm Zx = 450 Zz = 152 Sx = 497 Sz = 231 py = 250 Mpa Depth of shear-key considered = 200 mm Grout thickness = 25 mm Effective embedment of shear-key = 175 mm Size of weld between shear-key & base-p 8 mm (between flange and b 6 mm (between web and base Pedestal size : 650 mm 650 mm Capacity of the shear key from concrete crushing consideration : Along longitudinal dire 203.20 x 175 x 18.00 640080 N 640.08 kN Along transverse direct 203.60 x 175 x 18.00 641340 N 641.34 kN N/mm 2 N/mm 2 Considering fshear = tf = tw = cm 3 cm 3 cm 3 cm 3 LP = BP = Ftrans Flong X Z LP BP
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Design of Shear Key
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shear keyxxxDESIGN OF SHEAR-KEY BELOW COLUMN BASE-PLATESummaryRemarksActual longitudinal shear force =300kNL/C :Longitudinal shear capacity =307.9kNo.k.Actual transverse shear force =93kNnode :Transverse shear capcity =219.5kNo.k.Max longitudinal shear =300kNGrade of concrete =30MPaMax transverse shear =116kNCrushing strength (per BS 5950, Cl. 4.13.2.1) =Max interaction =1.400.6 x 30 MPa=18N/mm2Shear strength (per ACI-318) =4 x 0.85 x ( 30 x 145.038 x 0.8 ) ^ 0.5 psi=200.6psi=1.38N/mm2Considering fshear =0.85(Concrete characteristic cube strength converted to cylinder strengthby multiplying with a factor of 0.8)Shear Key Section :Member =UC203x203x46D =203.2mmB =203.6mmtf =11mmtw =7.2mmZx =450cm3Zz =152cm3Sx =497cm3Sz =231cm3py =250MpaDepth of shear-key considered =200mmGrout thickness =25mmEffective embedment of shear-key =175mmSize of weld between shear-key & base-plate =8mm(between flange and base plate)6mm(between web and base plate)Pedestal size :LP =650mmBP =650mmCapacity of the shear key from concrete crushing consideration :Along longitudinal direction =203.20 x 175 x 18.00=640080N=640.08kNAlong transverse direction =203.60 x 175 x 18.00=641340N=641.34kNCapacity of the shear key from weld strength consideration :Total weld area =(2 x (203.20-2 x 11) x 6 + 4 x 203.60*8 + 2 x (2 x 11-7.20 - 2 x 6) x 8) x 0.7=6114.08mm2(effective in resisting direct shear)M.I of weld about Z =( (1/12) x 203.60 ^3 x 4 - (1/12) x ( 7.20 + 2 x 6 ) ^3 x 2 + 4 x 11.00 x ( 203.60 /2 ) ^2 ) x 0.7 x 8 +( 2 x ( 203.20 - 2 x 11.00 ) x ( 7.20 / 2 ) ^ 2 ) ) x ( 0.7 x 6 )=18320958.1mm4M.I of weld about X =( 203.60 x (( 203.20 / 2 ) ^2 ) x 2 + ( 203.60 - 7.20 - 2 x 6 ) x ( ( 203.20 / 2 - 11.00 ) ^ 2 ) x 2) x 0.7 x8+ ( 1 / 12 ) x ( ( 203.20-2 x 11) ^ 3 ) x 2 x ( 0.7 x 6 )+( 4 x 1/12 x 11 ^ 3 + 4 x 11 x ( (203.2-11 ) / 2) ^2 ) x ( 0.7 x 8 )=46933935.6mm4Let the maximum force along longitudinal direction =340.4799446429kNLet the maximum force along transverse direction =749.9340617827kNMaximum direct longitudinal shear stress in weld =340.48 x 1000 / ( 6114.1 )=55.6878458644N/mm2Maximum direct transverse shear stress in weld =749.93 x 1000 / ( 6114.1 )=122.656893888N/mm2Maximum tension in weld due to moment created by long. shear =[ 340.5 x 1000 x ( 175 / 2 + 25 ) ] x ( 203.6 / 2 ) / 18320958.1=212.8352974085N/mm2Maximum tension in weld due to moment created by transv. shear =[ 749.9 x 1000 x ( 175 / 2 + 25 ) ] x ( 203.2 / 2 ) / 46933935.6=182.6342968387N/mm2Resultant longitudinal shear in weld =[ ( 55.7 ) ^ 2 ) + ( 212.8 ) ^ 2 ) ] ^ 0.5=220N/mm2
