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Concrete Shear Wall to ACI 318

Verified by the CalcTree engineering team on October 31, 2024

This calculator performs capacity checks for a concrete unbraced shear wall. It checks axial and shear, calculates second-order effects in order to check in-plane bending and plots the interaction diagram to check flexural-compression combined actions.
This calculation has been written in accordance with ACI 318-19.

Results Summary

Summary 
Design Check
Action
Resistance
Utilisation
Status
Shear Strength
V = 224.81 kips ΦVn = 237.21 kips
0.95 dimensionless
🟢
Axial Strength
N = 1124.04 kips ΦPn = 1999.19 kips
0.56 dimensionless
🟢
Flexural Strength
M = 1475.12 kips ΦMn = 2155.43 kips
0.56 dimensionless
🟢
Can’t display the image because of an internal error. Our team is looking at the issue.



Calculation

Technical notes

  1. Maximum strain at the extreme concrete compression fiber shall be assumed to be equal to 0.003 (ACI 318 22.2.2.1).
  2. The tensile strength of concrete shall be neglected in flexural and axial strength calculations (ACI 318 22.2.2.2).
  3. This calculator considers unbraced walls that cantilever from the ground, braced walls are not considered.
  4. The user inputted design moment
    
    shall be the first-order design moment. Second-order effects are automatically accounted for through the calculation of
    
    .

1. Properties

1.1 Materials



fpc
:4,000 psi​



wc
:145 lb / ft^3​



Ec
:110,429 ksi​






Es
:29,000 ksi​



fy
:60 ksi​



1.2 Geometry



lw
:9.00 ft​



hw
:50.00 ft​



h
:8.00 in​






1.3 Reinforcement

Vertical reinforcement:


db,v
:#4​



s,v
:1.00 ft​



layers
:2​



cover
:1.00 in​


Horizontal reinforcement:


db,h
:#4​



s,h
:2.00 ft​




2. Design Actions



Nu
:1,000.0 kips​



Mu
:1,000.0 kips ft​



Vu
:200.0 kips​

Note, a positive values for

is compression, and a negative value is tension.





3. Design Checks

3.1 Shear Strength

According to ACI 318 Ch 11.5.4.2, the shear capacity

at any horizontal section shall not exceed

and shall be calculated by:

ϕVn=0.75(αcλfc′+ρtfyt)Acv\phi V_n = 0.75(α_c λ\sqrt{f'_c} + ρ_t f_{yt})A_{cv}
Where:
  1. 
    
    
  2. 
    
    is the factored axial force normal to cross-section occurring simultaneously with
    
    or
    
    ; to be taken as positive for compression and negative for tension.
  1. 
    
    is the ratio of the area of distributed transverse reinforcement to the gross concrete area perpendicular to that reinforcement.
  2. 
    
    is the gross area of the concrete section bounded by web thickness and length of the section in the direction of the shear force considered.


hw/lw
:5.56​



αc
:2.00​




Ch 11.5.4.3


Acv
:864 in^2​





ρt
:0.00​






Vn
:321.35 kip​




Ch 11.5.4.3


ΦVn
:241.01 kip​




Table 21.2.1


Shear utilization
:0.83 🟢​






3.2 Axial Strength

3.2.1 Maximum axial compressive strength
At a low load application rate, the accepted compressive strength for the concrete is 0.85 times the specified compressive strength that is

.
The ultimate axial strength of the element is attained when the concrete undergoes crushing failure, and the reinforcement steel yields:

Pn=0.8PoPn = 0.8 P_o

Po=0.85fc′(Ag−Ast)+fyAstP_o = 0.85f'_c(A_g-A_{st})+f_yA_{st}
Where:
  1. 
    
    is the nominal axial compressive strength of the member.
  2. 
    
    is the nominal axial strength at zero eccentricity.
  3. 
    
    is the gross area of the concrete section.
  4. 
    
    is the total area of longitudinal reinforcement.

3.2.2 Maximum axial tensile strength
The concrete is fully fissured when the ultimate axial tensile strength is reached, rendering its contribution null. Therefore, the ultimate strength is attained when the reinforcement reaches its yield stress.

Pnt=fyAsP_{nt} = f_y A_s


Pn
:1,006.87 kip​




Ch 22.4.2.2


ΦPn
:1,659.14 kip​






Pnt
:-212.06 kip​




Ch 22.4.3.1


ΦPnt
:-190.85 kip​






Axial utilization
:0.60 🟢​






3.3 Second-order effects

As per Chapter 6.6.4.5.1, the second-order moment used for the design of columns and walls,

, shall be the first-order moment

amplified for the effects of the member curvature, given by:

Mc=δMuM_c = \delta M_u
Where:
  1. 
    
    is the axial force applied to the wall.
  2. 
    
    is the magnification factor, given by
    
    
  3. 
    
    is the critical buckling load, given by
    
    
  4. 
    
    is the concrete modulus of elasticity.
  5. 
    
    is the moment of inertia of the gross concrete section about the centroidal axis, neglecting reinforcement.
  6. 
    
    is the effective length factor, and for walls is recommended that a
    
    value of
    
    is used (R6.6.4.4.3)


Pc
:3.49 kilokip​




Ch 6.6.4.4.2


δ
:1.62​




Ch 6.6.4.5.2


Mc
:1,618.92 ft kip​




Ch 6.6.4.5.1


3.4 Flexural Strength

The nominal moment capacity

, is expressed as the sum of the moments from the internal forces, taking into account the stress distribution within the section. The equation for the nominal moment in a reinforced concrete column under eccentric axial loading is:

Mn=Pne=0.85fc′ a lw(h2−a2)+fs′As′(h2−d′)+fsAs(d−h2)M_n = P_n e = 0.85 f'_c \ a \ l_w ( \frac{h}{2} - \frac{a}{2} ) + f'_s A'_s ( \frac{h}{2} - d' ) + f_s A_s ( d - \frac{h}{2})
Where:
  1. 
    
    is the eccentricity for the axial load
  2. 
    
    is the distance from the fiber of maximum compressive strain.
  3. 
    
    is the equivalent rectangular concrete stress distribution.
  4. 
    
    is the distance from the fiber of maximum compressive strain to the neutral axis.
  1. 
    
    is the strength for reinforcement in tension.
  1. 
    
    is the strength for reinforcement in compression.


This equation sums the moments produced by the concrete and steel in compression, along with the steel in tension, taking into account their respective distances from the neutral axis of the section.
The value for

is multiplied by the strength reduction factor

, which varies from

in the compression behavior to

in tension. This can be better visualized in the interaction diagram. The value for

that is provided is the point on the interaction diagram that corresponds to the user inputted axial force demand

,



ΦMn
:2,371.51 ft kip​




Ch 22.2.2


Flexural utilization
:0.68 🟢​






3.5 Interaction Diagram

The interaction diagram for shear walls represents the relationship between nominal axial load

and nominal moment

, showing how the shear wall’s capacity changes under different axial force and bending moment combinations. In this diagram, the curve defines the safe limits of loading, where each point corresponds to a specific combination of

and

that the shear wall can resist without failure.


Can’t display the image because of an internal error. Our team is looking at the issue.



Related Resources

  1. Concrete Shear Wall to AS3600
  2. Concrete Column P-M Diagram Calculator to ACI
  3. Column Buckling Calculator