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8.7 Calculate the axial compression capacity of the reinforced concrete columns for the following cases: transverse reinforcement: square ties 0 P = 0.80 Ø [0.85 f'Ag + (fy − 0.85 fé)Ast] -0.65 transverse reinforcement: round spirals OP=0.850 [0.85 fAg+ (fy - 0.85 fe) Ast] $=0.75 a) Square column with tied transverse reinforcement: 24° 8814 vert, bars 0.00 Vert. bars b) Round column with spiral reinforcement: 200 Column Section 14-39 Vert. P5 spral 24° c) Elongated round column with spiral reinforcement: Column Section 2¹-6°Ø Column Section fc' = 4 ksi, (concrete compressive strength) fy = 60 ksi (steel yield strength) Ag - gross concrete area Ast = area of vertical steel

8.7 Calculate the axial compression capacity of the reinforced concrete columns for the following cases: transverse reinforcement: square ties 0 P = 0.80 Ø [0.85 f'Ag + (fy − 0.85 fé)Ast] -0.65 transverse reinforcement: round spirals OP=0.850 [0.85 fAg+ (fy - 0.85 fe) Ast] $=0.75 a) Square column with tied transverse reinforcement: 24° 8814 vert, bars 0.00 Vert. bars b) Round column with spiral reinforcement: 200 Column Section 14-39 Vert. P5 spral 24° c) Elongated round column with spiral reinforcement: Column Section 2¹-6°Ø Column Section fc' = 4 ksi, (concrete compressive strength) fy = 60 ksi (steel yield strength) Ag - gross concrete area Ast = area of vertical steel

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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8.7 Calculate the axial compression capacity of the reinforced concrete columns for the following cases: transverse reinforcement: square ties P₁ = 0.80 [0.85 fAg + (fy -0.85 fé) Ast] $=0.65 transverse reinforcement: round spirals Ø P = 0.85 0 [0.85 f Ag + (fy -0.85 fe) Ast] $=0.75 a) Square column with tied transverse reinforcement: 8 #14 vert. bars 8-40 Vert. bars b) Round column with spiral reinforcement: #4 spiral 24" Column Section 14-49 Vert, bar #5 spral- 200 ✓24" c) Elongated round column with spiral reinforcement: Column Section 2'-6" Ø 20⁰ Ø Column Section fc' = 4 ksi, (concrete compressive strength) fy = 60 ksi (steel yield strength) Ag - gross concrete area Ast = area of vertical steel
Transcribed Image Text:8.7 Calculate the axial compression capacity of the reinforced concrete columns for the following cases: transverse reinforcement: square ties P₁ = 0.80 [0.85 fAg + (fy -0.85 fé) Ast] $=0.65 transverse reinforcement: round spirals Ø P = 0.85 0 [0.85 f Ag + (fy -0.85 fe) Ast] $=0.75 a) Square column with tied transverse reinforcement: 8 #14 vert. bars 8-40 Vert. bars b) Round column with spiral reinforcement: #4 spiral 24" Column Section 14-49 Vert, bar #5 spral- 200 ✓24" c) Elongated round column with spiral reinforcement: Column Section 2'-6" Ø 20⁰ Ø Column Section fc' = 4 ksi, (concrete compressive strength) fy = 60 ksi (steel yield strength) Ag - gross concrete area Ast = area of vertical steel
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Answer 

(a) Calculation of axial compression capacity of the square column

To calculate the axial compression capacity with square ties we are given

ϕ.Pn = ϕ*0.80(0.85*f'c*Ag+(fy-0.85*f'c)*Ast))

ϕ= strength reduction factor

ϕ= 0.65

f'c = compressive strength of concrete

f'c = 4 ksi

Ag = gross section area

Ag = 24*24

Ag = 576 in2 

fy = yield strength of steel

fy = 60 ksi

Ast = Area of steel bars

Ast =18 in2     (from areas of group of standard bars for 8-#14)

Now substitute the values to get 'ϕ.Pn'

ϕ.Pn = ϕ*0.80(0.85*f'c*Ag+(fy-0.85*f'c)*Ast))

ϕ.Pn = 0.65*0.80(0.85*4*576+(60-0.85*4)*18))

ϕ.Pn = 1548.144 kips

" axial compression capacity of the square column = 1548.144 kips "

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