Column Masonry Design

Project: {{ outputs.project }}

Designed by: {{ outputs.designer }}

Emitted on: {{ outputs.date }}

Design Standard: CSA S304-24

Column Data:

Section Type: {{ outputs.ColType }}

{{ outputs.sectim_html}}{{ outputs.table_html }}

Geometry:

{{ "b" | katex }} = {{ outputs.colb | katex}} mm

{{ "t" | katex }} = {{ outputs.colt | katex }} mm

{{ "h" | katex }} = {{ outputs.ColH | katex }} mm

cover_x = {{ outputs.cx | katex }} mm

cover_y = {{ outputs.cy | katex}} mm

Masonry Properties:

{{ "{f'}_m" | katex }} = {{ outputs.masonrystr | katex}} MPa (CL 6.1.1)

{{ "{E}_m" | katex }} = {{ outputs.ModEm | katex}} MPa (CL 7.5.2)

{{ "{f}_t" | katex }} = {{ outputs.ft | katex}} MPa (Table 5)

Steel Properties:

{{ "{E}_s" | katex }} = {{ outputs.ModEs | katex}} MPa (CL 7.5.1)

{{ "{f}_y" | katex }} = {{ outputs.fy | katex}} MPa (CL 6.5)

Rebar = {{ outputs.barSize | katex}}

{{ "{A}_s" | katex }} = {{ outputs.Asprovided | katex}} mm²

Tie = {{ outputs.tieD | katex}} mm

Tie Spacing = {{ outputs.tieS | katex}} mm

Factors:

{{ "{\\phi_s}" | katex }} = {{"0.85" | katex}} (CL 5.3.2.2)

{{ "{\\phi_m}" | katex }} = {{"0.60" | katex}} (CL 5.3.2.1)

{{ "{\\phi_{er}}" | katex }} = {{"0.75" | katex}} (CL 5.3.4)

Preliminary Calculations:

Loading:

Total Axial Load ULS and SLS:

{{ "{w_{f,x}}" | katex }} = {{ outputs.wfx | katex}} kN/m (NBCC Table 4.1.3.2-B 0.4*W)

{{ "{w_{s,x}}" | katex }} = {{ outputs.wsx | katex}} kN/m (NBCC Table 4.1.3.4 0.3*W)

{{ "{w_{f,y}}" | katex }} = {{ outputs.wfy | katex}} kN/m (NBCC Table 4.1.3.2-B 0.4*W)

{{ "{w_{s,y}}" | katex }} = {{ outputs.wsy | katex}} kN/m (NBCC Table 4.1.3.4 0.3*W)

{{ "{P_{f}}" | katex }} = {{ outputs.Pf | katex}} kN (CL 5.2.2 1.25D+1.5L)

{{ "{P_{s}}" | katex }} = {{ outputs.Ps | katex }} kN (CL 5.2.3 DL+LL)

{{ "{e_{x}}" | katex }} = {{ outputs.eccx | katex}} mm

{{ "{e_{y}}" | katex }} = {{ outputs.eccy | katex}} mm

Cross-Sectional Properties:

{{ "{A_{col}}" | katex }} = {{ outputs.Acol | katex}} mm²

X-direction:

{{ "{k_{x}}" | katex }} = {{ outputs.kx | katex}} (Table B.1)

{{ "{I_{o,x}}" | katex }} = {{ outputs.Iox | katex}} mm⁴

{{ "{I_{cr,x}}" | katex }} = {{ outputs.Icrx | katex }} mm⁴

Effective Stiffness:

{{ "EI_{eff} = E_m[ 0.25I_{o}-(0.25I_{o}- I_{cr})\\frac{e_v - e_k}{2e_k}]" | katex }} = {{ outputs.EIeffx | katex}} Nmm²(CL 11.7.4.4)

where:

{{ "e_v = \\frac{M_{fp}}{P_f}" | katex }} mm

{{ "e_k = \\frac{S_e}{A_e}" | katex }} mm

{{ "S_ke = \\frac{I_o}{0.5t}" | katex }} mm³

Shear Force Diagram

{{ outputs.SFDX}}

Bending Moment Diagram

{{ outputs.BMDX }}

Y-direction:

{{ "{k_{y}}" | katex }} = {{ outputs.ky | katex }} (Table B.1)

{{ "{I_{o,y}}" | katex }} = {{ outputs.Ioy | katex }} mm⁴

{{ "{I_{cr,y}}" | katex }} = {{ outputs.Icry | katex }} mm⁴

Effective Stiffness:

{{ "EI_{eff} = E_m[ 0.25I_{o}-(0.25I_{o}- I_{cr})\\frac{e_v - e_k}{2e_k}]" | katex }} = {{ outputs.EIeffy | katex }} Nmm² (CL 11.7.4.4)

Where:

{{ "e_v = \\frac{M_{fp}}{P_f}" | katex }} mm

{{ "e_k = \\frac{S_e}{A_e}" | katex }} mm

{{ "S_ke = \\frac{I_o}{0.5t}" | katex }} mm³

Shear Force Diagram

{{ outputs.SFDY }}

Bending Moment Diagram

{{ outputs.BMDY }}

Strength Calculations:

Maximum factored axial load resistance:

{{ "P_{r,\max} = 0.80[ 0.85 \\phi_m f'_m (A_e - A_{st}) + \\phi_s f_y A_{st}]" | katex }} = {{ outputs.Prmax | katex}} kN (CL 11.4.2)

X-direction

Primary Moment:

{{ "{M_{p,x}}" | katex }} = {{ outputs.Mfx | katex }} kNm

Buckling Load:

{{ "P_{cr} = \\frac{\\pi^2\\phi_{er}EI_{eff}}{(1+\\beta_d)(kh)^2}" | katex }} = {{ outputs.Pcrx | katex}} kN (CL 11.7.4.3)

Where:

{{ "\\beta_d = \\frac{M_{Pf_{dead}}}{M_{Pf_{total}}}" | katex }}

Magnification Factor:

{{ "\\psi_{u} = \\frac{C_m}{1 - \\frac{P_f}{P_{cr}}}" | katex }} = {{ outputs.psix | katex }} (CL 11.7.4.3)

Where:

{{ "{C_m} = \\frac{M_1}{M_2}" | katex }} (CL 10.7.4.5)

Total Moment:

{{ "{M_{ftot}} = M_{fp} \\psi_u" | katex }} = {{ outputs.Mftx | katex }} kNm (CL 11.7.4.3)

Interaction Diagram

{{ outputs.diagramx }}

Y-direction

Primary Moment:

{{ "{M_{p,y}}" | katex }} = {{ outputs.Mfy | katex }} kNm

Buckling Load:

{{ "P_{cr} = \\frac{\\pi^2\\phi_{er}EI_{eff}}{(1+\\beta_d)(kh)^2}" | katex }} = {{ outputs.Pcry | katex }} kN (CL 11.7.4.3)

Where:

{{ "\\beta_d = \\frac{M_{Pf_{dead}}}{M_{Pf_{total}}}" | katex }}

Magnification factor:

{{ "\\psi_{u} = \\frac{C_m}{1 - \\frac{P_f}{P_{cr}}}" | katex }} (CL 11.7.4.3)

Where:

{{ "{C_m} = \\frac{M_1}{M_2}" | katex }} (CL 10.7.4.5)

Then:

{{ "\\psi_{u,y}" | katex}} = {{ outputs.psiy | katex }} (CL 11.7.4.3)

Total Moment:

{{ "{M_{ftot}} = M_{fp} \\psi_u" | katex }} (CL 10.7.4.3)

{{ "M_{ftot,y}" | katex}} = {{ outputs.Mfty | katex }} kNm (CL 11.7.4.3)

Interaction Diagram

{{ outputs.diagramy }}

Design Checks:

Geometry Requirements

{{ "h" | katex }} = {{ outputs.ColH | katex }} mm

{{ "h_{limit}" | katex }} = {{ outputs.colheightlimit | katex}} mm (CL 3.1)

{{ "h > h_{limit}" | katex }} {% if outputs["ColH"]>outputs["colheightlimit"] %} (Ok) {% else %} (Not a column element: change dimension) {% endif %}

{{ "b" | katex }} = {{ outputs.colb | katex}} mm

{{ "b_{limit}" | katex }} = {{ outputs.LengthLim | katex}} mm (CL3.1)

{{ "b \\le b_{limit}" | katex }} {% if outputs["colb"]<outputs["LengthLim"] %} (Ok) {% else %} (Not a column element: change dimension) {% endif %}

Rebar Size

Rebar = {{ outputs.barSize | katex}}

Rebar Limit = {{ outputs.rebarlimit | katex}} (CL 13.1.2)

Rebar < Rebar Limit {% if outputs["barSize"]<outputs["rebarlimit"] %} (Safe) {% else %} (Not Safe) {% endif %}

Eccentricity Check

{{ "{e_{x, prov}}" | katex }} = {{ outputs.eccx | katex}} mm

{{ "{e_{limit,x}}" | katex }} = {{ outputs.elimit | katex}} mm (CL 8.7.3)

{{ "e_{x,prov} > e_{limit,x}" | katex }} {% if outputs["eccx"]>=outputs["elimit"] %} (Ok) {% else %} (Assume limit eccentricity) {% endif %}

{{ "{e_{y, prov}}" | katex }} = {{ outputs.eccy | katex}} mm

{{ "{e_{limit,x}}" | katex }} = {{ outputs.elimit | katex}} mm (CL 8.7.3 )

{{ "e_{y,prov} > e_{limit,x}" | katex }} {% if outputs["eccy"]>=outputs["elimit"] %} (Ok) {% else %} (Assume limit eccentricity) {% endif %}

Slenderness Calculation

{{ "Sl_x=(10-3.5\\frac{M_{1x}}{M_{2x}})" | katex }}

{{ "Sl_x" | katex }} = {{ outputs.sx }}

{{ "Sl_{lower, lim}" | katex }} = {{ outputs.sxlowlim | katex}} (CL 11.7.3.3.1)

{{ "Sl_{upper, lim}" | katex }} = {{ outputs.sxuplimit | katex}} (CL 11.7.3.3.1)

{{ "Sl_x \\le Sl_{lower, lim}" | katex }} {% if outputs["sx"]<outputs["sxlowlim"] %} (Not slender) {% else %} (slightly slender) {% endif %}

{{ "Sl_x > Sl_{upper, lim}" | katex }} {% if outputs["sx"]>outputs["sxuplimit"] %} (Slender Element) "Warning": CL 10.9.2: Maximum slender shall not exceed 30 {% else %} (slightly slender) {% endif %}

{{ "Sl_y" | katex }} = {{ outputs.sy }}

{{ "Sl_{lower, lim}" | katex }} = {{ outputs.sylowlim | katex}} (CL 11.7.3.3.1)

{{ "Sl_{upper, lim}" | katex }} = {{ outputs.syuplim | katex}} (CL 11.7.3.3.1)

{{ "Sl_y \\le Sl_{lower, lim}" | katex }} {% if outputs["sy"]<outputs["sylowlim"] %} (Not slender) {% else %} (slightly slender) {% endif %}

{{ "Sl_y > Sl_{upper, lim}" | katex }} {% if outputs["sy"]>outputs["sxuplimit"] %} (Slender Element) "Warning": CL 10.9.2: Maximum slender shall not exceed 30 {% else %} (slightly slender) {% endif %}

Stiffness Limits

{{ "{EI_{eff,x}}" | katex }} = {{ outputs.EIeffrealx | katex }} Nmm²(CL 11.7.4.4)

{{ "{EI_{o,x}}" | katex }} = {{ outputs.EIglimx | katex }} Nmm²

{{ "{EI_{cr,x}}" | katex }} = {{ outputs.EIcrxLim | katex }} Nmm²

{{ "{EI_{cr,x}< EI_{eff,x} < 0.25EI_{o,x} }" | katex }} {% if outputs["EIeffx"]>outputs["EIcrxLim"] and outputs["EIeffx"]<outputs["EIglimx"] %} (Ok) {% elif outputs["EIeffx"]<outputs["EIcrxLim"] and outputs["EIcrxLim"]<outputs["EIglimx"] %} (Take EIcr) {% else %} (Take EIg) {% endif %}

{{ "{EI_{eff,y}}" | katex }} = {{ outputs.EIeffrealy | katex }} Nmm²(CL 11.7.4.4)

{{ "{EI_{o,y}}" | katex }} = {{ outputs.EIglimy | katex}} Nmm²

{{ "{EI_{cr,y}}" | katex }} = {{ outputs.EIcryLim | katex}} Nmm²

{{ "{EI_{cr,y}< EI_{eff,y} < 0.25EI_{o,x} }" | katex }} {% if outputs["EIeffy"]>outputs["EIcryLim"] and outputs["EIeffy"]<outputs["EIglimy"] %} (Ok) {% elif outputs["EIeffy"]<outputs["EIcryLim"] and outputs["EIcryLim"]<outputs["EIglimy"] %} (Take EIcr) {% else %} (Take EIg) {% endif %}

Buckling Load

{{ "P_{cr,x} = \\frac{\\pi^2\\phi_{er}EI_{eff}}{(1+\\beta_d)(kh)^2}" | katex }} = {{ outputs.Pcrx | katex}} kN (CL 11.7.4.3)

{{ "P_{cr}>P_{f}" | katex }} {% if outputs["Pcrx"]>outputs["Pf"]%} (Ok) {% else %} (Not safe) {% endif %}

{{ "P_{cr,yy} = \\frac{\\pi^2\\phi_{er}EI_{eff}}{(1+\\beta_d)(kh)^2}" | katex }} = {{ outputs.Pcry | katex}} kN (CL 11.7.4.3)

{{ "P_{cr}>P_{f}" | katex }} {% if outputs["Pcry"]>outputs["Pf"]%} (Ok) {% else %} (Not safe) {% endif %}

Uniaxial Resistance

{{ "M_{r,x}" | katex}} = {{ outputs.Mrx | katex }} kNm (CL 11.9.2)

{{ "M_{ftot,x}" | katex}} = {{ outputs.Mftx | katex }} kNm

{{ "M_{ftot,x} > M_{r,x}" | katex }} {% if outputs["Mrx"]>outputs["Mftx"] %} (Safe) {% else %} (Not Safe) {% endif %}

{{ "M_{r,y}" | katex }} = {{ outputs.Mry | katex }} kNm (CL 11.9.2)

{{ "M_{ftot,y}" | katex }} = {{ outputs.Mfty | katex }} kNm

{{ "M_{ftot,x} > M_{r,x}" | katex }} {% if outputs["Mry"]>outputs["Mfty"] %} (Safe) {% else %} (Not Safe) {% endif %}

{{ "{P_r}" | katex }} = {{ outputs.Prmax | katex }} kN (CL 11.9.2)

{{ "{P_f}" | katex }} = {{ outputs.Pf | katex }} kN

{{ "P_{r,max} > P_f" | katex }} {% if outputs["Prmax"]>outputs["Pf"] %} (Safe) {% else %} (Not Safe) {% endif %}

Biaxial Resistance

{{ "\\frac{M_{fx.total}}{M_{r,x}} + \\frac{M_{fy.total}}{M_{r,y}} \\leq 1" | katex}} (CL 11.9.3)

{{ "\\frac{M_{fx.total}}{M_{r,x}} + \\frac{M_{fy.total}}{M_{r,y}}" | katex}} = {{ outputs.Mratio | katex }} {% if outputs["Mratio"]<=1 %} (Safe) {% else %} (Not Safe) {% endif %}

Deflections

(a) {{ "{M_{s} \\leq M_{cr}}" | katex }}

{{ "{\\Delta_s = \\frac{5M_sh^2}{48E_mI_o}}" | katex }} {% if outputs["Mcrx:"]< outputs["Msx"]%} (Use this condition) {% else %} (Use (b) condition) {% endif %}

(b) {{ "{M_{cr} < M_{s}}" | katex }}

{{ "{\\Delta_s = \\frac{5M_sh^2}{48E_mI_o} + \\frac{5(M_s - M_{cr})^2}{48E_mI_{cr}}}" | katex }}

Where:

{{ "{M_{cr} = \\frac{f_t + f_{cs}}{y_t} I_o}" | katex }}

{{ "{M_{s,x}}" | katex }} = {{ outputs.Msx | katex }} kNm

{{ "{\\Delta_{x}}" | katex }} = {{ outputs.deltaX }} mm (CL 11.14.1 )

{{ "{\\Delta_{x,lim}}" | katex }} = {{ outputs.allowdx | katex }} mm (CL 11.14.2)

{{ "{\\Delta_{x} \\le \\Delta_{x,lim}}" | katex }} {% if outputs["deltaX"]<outputs["allowdx"] %} (Safe) {% elif outputs["deltaX"]=="N/A" %} (Not Applicable) {% else %} (Not Safe) {% endif %}

{{ "{M_{s,x}}" | katex }} = {{ outputs.Msx | katex }} kNm

{{ "{\\Delta_{y}}" | katex }} = {{ outputs.deltaY }} mm (CL 11.14.1 )

{{ "{\\Delta_{y,lim}}" | katex }} = {{ outputs.allowdy | katex }} mm (CL 11.14.2)

{{ "{\\Delta_{y} \\le \\Delta_{y,lim}}" | katex }} {% if outputs["deltaY"]<outputs["allowdy"] %} (Safe) {% elif outputs["deltaY"]=="N/A" %} (Not Applicable) {% else %} (Not Safe) {% endif %}

Reinforcement Requirements (Vertical)

{{ "{A}_{s,min}" | katex }} = {{ outputs.Asmin | katex }} mm²(CL 11.15.1.1)

{{ "{A}_{s,max}" | katex }} = {{ outputs.Asmax | katex }} mm²(CL 11.15.1.1)

{{ "{A}_{s,prov}" | katex }} = {{ outputs.Asprovided }} mm²

{{ "{A_{s,min} \\le A_{prov}}" | katex }}{% if outputs["Asprovided"]>outputs["Asmin"] %} (Safe) {% else %} (Needs More reinforcement) {% endif %}

{{ "{A_{s,max} > A_{prov}}" | katex }}{% if outputs["Asprovided"]<outputs["Asmax"] %} (Safe) {% else %} (Needs Less reinforcement) {% endif %}

Reinforcement Requirements (Horizontal)

Tie Spacing = {{ outputs.tieS | katex}} mm (CL 13.2.1)

{{ "16d_b" | katex }} = {{ outputs.ties2 | katex }} mm

Tie Spacing < 16d_b{% if outputs["tieS"]<outputs["ties2"] %} (Ok) {% else %} (Decrease the Tie Spacing) {% endif %}

{{ "48d_{Tie}" | katex }} = {{ outputs.ties1 | katex }} mm

Tie Spacing < 48d_Tie {% if outputs["tieS"]<=outputs["ties1"] %} (Ok) {% else %} (Needs less Spacing) {% endif %}

Least column dimension = {{ outputs.ties3 | katex }} mm

Tie Spacing < least column dimension {% if outputs["tieS"]<outputs["ties2"] %} (Ok) {% else %} (Needs less Spacing) {% endif %}

Shear Strength

Masonry Shear strength (CL 11.10.3 .2)

{{ "v_{m} = 0.16(2 - \\frac{M_f}{V_fd_v})\\sqrt{f'_m}" | katex }}

Where:

{{ "d_{v} \\leq 0.8l_w" | katex }} (CL 3.2.2)

Then:

{{ "v_{m,x}" | katex }} = {{ outputs.Vmx | katex }} MPa

{{ "v_{m,y}" | katex }} = {{ outputs.Vmy | katex }} MPa

Factored Shear Resistance (CL 11.10.3 .1)

{{ "V_{r} = \\phi_m(v_mb_wd_v + 0.25P_d)\\gamma_d + (0.6\\phi_sA_vf_y\\frac{d_v}{d_v})" | katex }}

Where:

{{ "A_{v}" | katex }} = cross sectional area of shear reinforcement, mm²

{{ "s" | katex }} = vertical spacing of horizontal shear reinforcement, mm (CL 10.1.4.1)

{{ "P_d" | katex }} = axial compressive load on the section under consideration, N

{{ "\\gamma_g" | katex }} =1 for fully grouted masonry

{{ "V_{r,limit} = 0.4\\phi_m\\sqrt{f'_m}b_wd_v\\gamma_g" | katex }}

Then:

{{ "V_{r,x}" | katex }} = {{ outputs.Vrx | katex }} kN

{{ "V_{r,x,limit}" | katex }} = {{ outputs.Vrxlimi | katex }} kN

{{ "V_{r,x} \\le V_{r,x,limit}" | katex }} {% if outputs["Vrx"]<outputs["Vrxlimi"] %} {{ outputs.Vrx | katex }} kN {% else %} {{ outputs.Vrxlimi | katex }} kN {% endif %}

{{ "V_{f,x} \\le V_{r,x}" | katex }} {% if outputs["Vfx"]<outputs["Vrx"] %} (Safe) {% else %} (Not Safe) {% endif %}

{{ "V_{r,y}" | katex }} = {{ outputs.Vry | katex }} kN

{{ "V_{r,y,limit}" | katex }} = {{ outputs.Vrylimi | katex }} kN

{{ "V_{r,y} \\le V_{r,y,limit}" | katex }} {% if outputs["Vry"]<outputs["Vrylimi"] %} {{ outputs.Vry | katex }} kN {% else %} {{ outputs.Vrylimi | katex }} kN {% endif %}

{{ "V_{f,y} \\le V_{r,y}" | katex }} {% if outputs["Vfy"]<outputs["Vry"] %} (Safe) {% else %} (Not Safe) {% endif %}

"This publication is intended for use by professionals who are knowledgeable and experienced in masonry and concrete design and construction, and who are competent to evaluate the limitations of the information provided herein. The publishers and contributors to these publications disclaim any and all responsibility and liability for the application of the information contained herein, and any injury or damages suffered as a result of the use or inability to use this information."

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Masonry Column Design 2024 V2.0

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