Evo Design - structural engineering Calculation No. 001-RC COLUMN INTERACTIVE ONLINE CALCULATION SHEET Project No. onlinestructuraldesign.com SAMPLE CALCULATION Project Title: Reinforced concrete column - interactive design spreadsheet Calc. By Date Rev. MN 16.04.2014 0 Subject RC Column Capacity - Axial Force Bending Moment Checked By Date Interaction (ACI318) CN 16.04.2014 InputÂ Output Column dimensions Moment capacity Reinforcement Column interaction diagram Materials (steel, concrete, bolts) RC Column Capacity - Axial Force - Bending Moment Interaction (ACI 318) Axial force - bending moment interaction -Â  ultimate limit state Column dimensions h = 15 in b = 15 in (parameters that can not be modified in the demo version) Ag = h * b = in2 RC Element Area Reinforcement cover in cover to the center of the bars d = in depth of bottom reinforcement (h- cover) dc = in depth of top reinforcement (h- cover) Tension side reinforcement # 3 4 5 6 7 8 9 10 11 14 18 bar size n = no of bars As = in2 area of tension reinforcement rtens.reinf = % percentage of tension reinforcement Compression side reinforcement # 3 4 5 6 7 8 9 10 11 14 18 bar size n = no of bars As.b = in2 area of compression reinforcement rcomp.reinf = % percentage of compression reinforcement As.t = As + As.b = in2 total area of reinforcement r = % element total percentage of reinforcement per ACI 318 Section 10.9.1 Reinf percentage should be between 0.01Ag and 0.08Ag Confinement reinforcement (tied or spiral) tied spiral Materials Concrete fc' = 2.5 3 3.5 4 5 6 7 8 9 10 ksi concrete characteristicÂ cylinder strength Reinforcement type see reinforcement types here Grade 40 50 60 75 fy = ksi reinforcement yield strength References: ACI318-05 - Building code requirements for structural concrete "" Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Reinforcement modulus of elasticity per ACI 318 Es = ksi Section 8.5.2 Modulus of elasticity of reinforcement Yield reinforcement strain: fy / Es = The relationship between concrete compressive stress and concrete strain is satisfied per ACI 318-05 by an equivalent rectangular concrete stress distribution defined by a 0.85*fc' uniform Sections 10.2.6 and 10.2.7 stress over an equivalent compression zone bounded by edges of the cross section and a straight line located parallel to the neutral axis at a distanceÂ  a = b1*cÂ  from the fiber ofÂ maximum compressive strain. Section strength reduction factor f =Â 0.90 For tension controlled sections per ACI 318-05 0.70 Compression controlled section with spiral reinforcement Section 9.3 0.65 Compression controlled section other reinforced members Â Values of f strength reduction factor Maximum usable strain at extreme concrete compression fiber is 0.003 per ACI 318-05 Section 10.2.3 Maximum usable strain at extreme concrete compression fiber shall be assumed equal to 0.003; The relation between concrete compressive stress andÂ concrete strain is assumed rectangular Section 10.2.7.1 0.85fc' value uniformly distributed over an equivalent compression zone bounded by edges of the cross section and a straigth line located parale to the neutral axis at a distance a = b1*c from the fiber of max. compression strain b1 = factor relating depth of equivalent per ACI 318-05 rectangular compressive stress block Section 10.2.7.3 to neutral axis depth between 2500 and 4000 psi b1 = 0.85, above 4000 b1 will be reduced lineary at a rate of 0.05 per 1000 psi but not lower than 0.65 a = b1 * c depth of equivalent rectangular Section 10.2.7.1 stress block Section 10.2.3 stress in reinforcement below fy shall be taken as Es times steel strain. For strains greater than that correspondingÂ to fy, stress in reinforcement shall be considered independent of strain and equal to fy. "" Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Point 1 - Pure compression f =Â compression controlled section Section strength reduction factor fPn,max =Â f[0.85fc'(Ag-Ast)+fyAst] per ACI 318 eq. 10-1 and 10-2 fPn,max =Â kips Maximum allowable value of the nominal axial strength of cross section multipliedÂ  by the strength reduction factor Point 2 - fs = 0 Concrete strain: Concrete has reached ultimate concrete design The neutral axis is located in the center of the bottom reinforcement compressive shortening strain andÂ  fs = 0 c = dÂ  = in Neutral axis location - in this case in the center of the bottom reinforcement Top reinforcement strain (compression): *(c-dc)/c= Yield reinforcement strain: => f =Â compression controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc )] fMn =Â ft -kips Point 3 - fs = 0.5 * fy Concrete strain: Concrete has reached ultimate concrete design Â compressive shortening strain andÂ  fs = 0.5 * fy Bottom reinforcement strain (tension): et = ( 0.5 * fy ) / Es = c = in From the relation [c / (d - c)] = 0.003 / et Top reinforcement strain (compression): *(c-dc)/c = Yield reinforcement strain: => f =Â compression controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b -Â  et * Es * As ] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + et * Es * As * (d - h/2)] fMn =Â ft -kips "" Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Point 4 - fs =Â  fy (Balanced point) per ACI 318-05 Concrete strain: Section 10.3.2 Concrete has reached ultimate concrete design Bottom reinforcement strain (tension): et = fy / Es = Â compressive shortening strain andÂ  tension reinforcement reaches the strain corresponding to fyÂ  (fs = fy) c = in From the relation [c / (d - c)] = 0.003 / et Top reinforcement strain (compression): *(c-dc)/c = Yield reinforcement strain: => f =Â compression controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b -Â  fy * As ] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)] fMn =Â ft -kips Point 4b - fs =Â  fy Transition from Compression controlled section to Tension Controlled per ACI 318-05 Concrete strain: Section 9.3.2.2 For sections in which the net tensile strain at nominal Bottom reinforcement strain (tension): et = fy / Es = strength et is between the limits for compression controlled ans tension controlled sections f will be linearly increased from that for compression controlled to 0.9 c = in From the relation [c / (d - c)] = 0.003 / et Top reinforcement strain (compression): *(c-dc)/c = Yield reinforcement strain: => f =Â transition from compression controlledÂ  to tension controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b -Â  fy * As ] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)] fMn =Â ft -kips "" Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Point 4c - fs =Â  fy Transition from Compression controlled section to Tension Controlled per ACI 318-05 Concrete strain: Section 9.3.2.2 Concrete has reached ultimate concrete design Bottom reinforcement strain (tension): et = fy / Es = compressive shortening strain andÂ  tension reinforcement is in transition from tension controlled to tensin controlled c = in From the relation [c / (d - c)] = 0.003 / et Top reinforcement strain (compression): *(c-dc)/c = Yield reinforcement strain: => f =Â transition from compression controlledÂ  to tension controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b -Â  fy * As ] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)] fMn =Â ft -kips Point 5 - et =Â  0.005 - tension controlled section Concrete strain: Concrete has reached ultimate concrete design compressive shortening strain andÂ  et has reached 0.005 Bottom reinforcement strain (tension): et = 0.0050 corresponding to f = 0.9 (tension controlled section) c = in From the relation [c / (d - c)] = 0.003 / et Top reinforcement strain (compression): *(c-dc)/c = Yield reinforcement strain: => f =Â tension controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b -Â  fy * As ] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)] fMn =Â ft -kips "" Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Point 6 - Pure Bending Concrete strain: Concrete has reached ultimate concrete design compressive shortening strain andÂ  et has reached 0.005 Bottom reinforcement strain (tension): et = corresponding to f = 0.9 (tension controlled section) c = in From the relation [c / (d - c)] = 0.003 / et Top reinforcement strain (compression): *(c-dc)/c = Yield reinforcement strain: => f =Â tension controlled section Section strength reduction factor a = b1 * c = in depth of equivalent rectangular stress block fPn =Â f *Â  [ 0.85* fc' * a * b + As.b -Â  fy * As ] fPn =Â kips fMn =Â f *Â  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)] fMn =Â ft -kips Point 7 - Maximum tension f =Â tension controlled section Section strength reduction factor fPn =Â Â = - f * fy * [As.b + As ] fPn =Â kips fMn =Â 0.00 ft -kips Data for the M-N interaction graph: Ncap Mcap Point 1 0.00 Point 2 Point 3 Point 4 Point 4b Point 4c Point 5 Point 6 Point 7 0.00 Neff Meff CO1 CO2 CO3