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Project : Prepared by: Date :
Job No.: Item: L06 P3 Shear cage S1 Checked by: Sheet no.: 1 of 5
This spreadsheet illustrates the punching shear check for Level 06 - column at grid K1-30 (shear cage S1)
The punching shear resistance for section in flexure is given in Technical report TR43 (section 6.11.2)
Concrete f cu := 45MPa
Reinforcement f y := 460MPa
Design shear Vdesign := 3180kN
Transverse direction
Panel width = 8.4m
Thanks to capitals, the equivalent section at critical perimeter is 420D (320+100) x 1000W (600+2*200)
Effective depth dtr := 420mm − ( 25mm + 16mm + 8mm) dtr = 371 ⋅ mm
Length of critical perimeter perpendicular to transverse direction
(
btr := 1000mm + 2 ⋅ 1.5 ⋅ dtr − 100mm ) btr = 1813 ⋅ mm
Area reinforcement provided (8T20 + 3 bonded tendons 5s)
3 ⋅ 5 ⋅ 110kN
Astr := 8T20 + 2
fy Astr = 6099 ⋅ mm
Width over which reinforcement provided in width
btr2 := 1000mm + 2 ⋅ 1.5 ⋅ 320mm btr2 = 1960 ⋅ mm
Area of reinforcement provided in width, btr
btr 2
Aspv := ⋅ Astr Aspv = 5642 ⋅ mm
btr2
Shear cage calculation Rev 0
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Project : Prepared by: Date :
Job No.: Item:L06 P3 Shear cage S1 Checked by: Sheet no.: 2 of 5
Concrete shear capacity
100Aspv
k1 := min , 3 k1 = 0.839
btr ⋅ dtr
k2 := max 1 ,
400mm
dtr
k2 = 1.078
1
1 1 3
0.79 3 fcu
4
νc := ⋅ k1 ⋅ k2 ⋅ ⋅ MPa νc = 0.739 ⋅ MPa
1.25 25MPa
Effects of prestress
−420mm
etr := + 45mm + 25mm
2 etr = −140 ⋅ mm
For Span width 8.4m
Prestress force/ tendon after all losses = 110kN
Number of tendon across panel width = 7*5=35
Prestress force across panel width
P := 35 ⋅ 110kN
P = 3850 ⋅ kN
Prestress force across critical perimeter, P1
P1 := 0.5 ⋅ P P1 = 1925 ⋅ kN
Area of concrete across panel width (8.4m) 2
Ac := 0.32m ⋅ 8.4m Ac = 2.688 m
2
( 320mm) 3
Zt := btr ⋅ Zt = 0.031 ⋅ m
6
Zt
M0 := 0.8 ⋅ P ⋅ − 0.8 ⋅ P1 ⋅ etr
Ac M0 = 251 ⋅ kNm
Shear cage calculation Rev 0
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Project : Prepared by: Date :
Job No.: Item: Checked by: Sheet no.: 3 of 5
Applied Moments and Shear Forces
Mtr := 1350kNm
Vtr := 1380kN
Vtr
Vcrtr := νc ⋅ btr ⋅ dtr + M0 ⋅ Vcrtr = 754 ⋅ kN Vtr
Mtr M0 ⋅ = 257 ⋅ kN
Mtr
Longitudinal direction
Panel width = 8.4m
Effective depth dlg := 420mm − ( 25mm + 8mm) dlg = 387 ⋅ mm
Length of critical perimeter perpendicular to longitudinal direction
(
blg := 1000mm + 2 ⋅ 1.5 ⋅ dlg − 100mm ) blg = 1861 ⋅ mm
Area reinforcement provided (8T20 + 3 bonded tendons 5s)
3 ⋅ 5 ⋅ 110kN
Aslg := 8T20 + 2
fy Aslg = 6099 ⋅ mm
Width over which reinforcement provided in width
blg2 := 1000mm + 3 ⋅ 320mm blg2 = 1960 ⋅ mm
Area of reinforcement provided in width, btr
blg 2
Aslg1 := ⋅ Aslg Aslg1 = 5791 ⋅ mm
blg2
Concrete shear capacity
100Aslg1
k1 := min , 3 k1 = 0.804
blg⋅ dlg
k2 := max 1 ,
400mm
dlg
k2 = 1.034
1
1 1 3
0.79 3 4 fcu
νc := ⋅ k1 ⋅ k2 ⋅ ⋅ MPa νc = 0.721 ⋅ MPa
1.25 25MPa
Shear cage calculation Rev 0
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Project : Prepared by: Date :
Job No.: Item: Checked by: Sheet no.: 4 of 5
Effects of prestress
−420mm
elg := + 25mm + 25mm
2 elg = −160 ⋅ mm
For Span width 8.4m
Prestress force/ tendon after all losses = 110kN
Number of tendon across panel width = 7*5=35
Prestress force across panel width
Plg := 35 ⋅ 110kN
Plg = 3850 ⋅ kN
Prestress force across critical perimeter, P1
P1lg := 0.6 ⋅ P P1lg = 2310 ⋅ kN
Area of concrete across panel width 2
(8.4m) Ac.lg := 0.32m ⋅ 8.4m Ac.lg = 2.688 m
2
( 320mm) 3
Zt.lg := blg ⋅ Zt.lg = 0.032 ⋅ m
6
Zt.lg
M0.lg := 0.8 ⋅ Plg ⋅ − 0.8 ⋅ P1lg ⋅ elg
Ac.lg M0 = 251 ⋅ kNm
Applied Moments and Shear Forces
Mlg := 1550kNm
Vlg := 1370kN
Vlg
Vcrlg := νc ⋅ blg ⋅ dlg + M0 ⋅
Mlg Vlg Vcrlg = 741 ⋅ kN
M0 ⋅ = 222 ⋅ kN
Mlg
Total shear resistance
Vcr := Vcrtr + Vcrlg Vcr = 1495 ⋅ kN
Shear cage calculation Rev 0
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Project : Prepared by: Date :
Job No.: Item: L06 P3 Shear cage S1 Checked by: Sheet no.: 5 of 5
Applied shear force
Longitudinal direction provides worst condition
Mlg
Veff := Vdesign ⋅ 1.0 + 1.5 ⋅
blg ⋅ Vlg Veff = 6080 ⋅ kN
Checkshear := "provide shear cage" if Veff ≥ Vcr
"shear cage not required" otherwise
Checkshear = "provide shear cage"
Asv required
Asv :=
( Veff − Vcr ) Asv = 10493 ⋅ mm
2
0.95 ⋅ f y
Using T16 double legs links, number required
Asv
No :=
2T16 No = 26
Maximum spacing permitted = 1.5d
Place 2x8 = 16 Nos at 150 spacing no on perimeter of 0.5d from the column face.
Place 6x8 = 48 Nos at 150 spacing no on perimeter of 2.25d from the column face.
Shear cage calculation Rev 0
