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ACI 318-14

Combined footing in accordance with ACI 318 (2014)


An Combined footing is a long footing supporting two or more columns in one row.  Combined footing are commonly used as alternative when columns are spaced too closely that if isolated footing is provided the soil beneath may have a part of common influence zone and bearing capacity of soil is such that isolated footing design will require extension of the column foundation to go beyond the property line.

SkyCiv Foundation Design module includes the design of combined footing conforming to the American Concrete Institute (ACI 318).

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Design of Isolated Foundation


Dimension Requirements

Determining the dimension of a isolated footing, it is applied (service) unfactored loads, such as DLWE, and etc in whatever combination that governs on design load over the allowable soil pressure based on the recommendation of ACI 318-14 Section 13.2.6

\(\text{q}_{\text{a}} = \frac{  \text{P1}_{\text{n}}  + \text{P2}_{\text{n}}  }{\text{A}} \rightarrow \) Equation 1

where:
qa = net allowable soil pressure
P1n = unfactor loads at Column 1 (left)
P2n = unfactor loads at Column 2 (right)
A = Foundation area

From Equation 1, qa are interchange with A.

\(\text{A} = \frac{ \text{P1}_{\text{n}} + \text{P2}_{\text{n}} }{\text{q}_{\text{a}}} \rightarrow \) Equation 1a

One-way Shear

The one-way shear or beam shear extends it critical section across the width of the footing and is located at a distance “d” from the face of a column, where Critical Plane Shear is located (Refer to Figure 1).

One way shear combined

Figure 1. Critical plane shear of One-way shear

The Shear Demand or Vu is calculated assuming the footing is cantilevered away from the column where the area is (red) hatch indicate in Figure 2 in accordance of ACI 318-14, Section 8.5.3.1.1.

\(\phi\text{V}_{\text{c}} = \phi _{\text{shear}} \times 2 \sqrt{\text{f’}_{\text{c}}} \times \text{b}_{\text{w}} \times \text{d} \rightarrow \) Equation 2 (ACI Eq. 22.5.5.1 English) 

or

\(\phi\text{V}_{\text{c}} = \phi _{\text{shear}} \times 0.17 \sqrt{\text{f’}_{\text{c}}} \times \text{b}_{\text{w}} \times \text{d} \rightarrow \) Equation 2 (ACI Eq. 22.5.5.1 Metric) 

where:
ϕshear = shear factor
f’c = specified compressive strength of concrete, psi or Mpa
bw = web width or diameter of circular section, in or mm
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in or mm

The Shear Capacity or ϕVc is calculated through equation 2 per ACI 318-14, Section 22.5.5.1.

\(\text{V}_{\text{u}} \leq  \phi\text{V}_{\text{c}} \rightarrow \) Equation 3 (ACI Eq. 7.5.1.1(b))

In skyCiv , In compliance of Equation 3, the calculation one-way shear ratio (Equation 4) is calculated by Shear Demand over Shear Capacity.

\( \text{ratio} = \frac{\text{Shear Demand}}{\text{Shear Capacity}} \rightarrow \) Equation 4

Two-way Shear

The two-way shear or punching shear extends it critical section across the perimeter width of the footing and is located at a distance “d/2” from the face of a column, where Critical Plane Shear is located (Refer to Figure 2).

Two way shear combined

Figure 2. Critical plane shear of Two-way shear

The Shear Demand or Vu is located at a distance of “d/2” where the (red) hatch area indicated in Figure 2 in accordance of ACI 318-14, Section 22.6.4.

\(\phi\text{V}_{\text{c}} = \phi _{\text{shear}} \times 4 \times \lambda \times \sqrt{\text{f’}_{\text{c}}} \rightarrow \) Equation 5 (ACI Eq. 22.6.5.2(a) English) 

\(\phi\text{V}_{\text{c}} =  \left ( 2 + \frac{4}{\beta } \right ) \times \lambda \times \sqrt{f’_{c}} \rightarrow \) Equation 6 (ACI Eq. 22.6.5.2(b) English)

\(\phi\text{V}_{\text{c}} = \left ( 2 + \frac{\alpha _{s} \times d }{b{o}} \right ) \times \lambda \times \sqrt{f’_{c}} \rightarrow \) Equation 7 (ACI Eq. 22.6.5.2(c) English)

or

\(\phi\text{V}_{\text{c}} = \phi _{\text{shear}} \times 0.33 \times \lambda \times \sqrt{\text{f’}_{\text{c}}} \rightarrow \) Equation 5 (ACI Eq. 22.6.5.2(a) Metric) 

\(\phi\text{V}_{\text{c}} = 0.17 \times \left ( 1 + \frac{2}{\beta } \right ) \times \lambda \times \sqrt{f’_{c}} \rightarrow \) Equation 6 (ACI Eq. 22.6.5.2(b) Metric)

\(\phi\text{V}_{\text{c}} = 0.0083 \times \left ( 2 + \frac{\alpha _{s} \times d }{b{o}} \right ) \times \lambda \times \sqrt{f’_{c}} \rightarrow \) Equation 7 (ACI Eq. 22.6.5.2(c) Metric)

note: β is the ratio of long side to short side of the column, concentrated load, or reaction area and αs is given 22.6.5.3

where:
λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength 
f’c = specified compressive strength of concrete, psi or Mpa
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.or mm

The Shear Capacity or ϕVc is calculated and governing the least of value through equation 5,6 and 7 per ACI 318-14, Section 22.6.5.2

\(\text{V}_{\text{u}} \leq  \phi\text{V}_{\text{c}} \rightarrow \) Equation 8 (ACI Eq. 7.5.1.1(b))

In skyCiv , In compliance of Equation 8, the calculation two-way shear ratio (Equation 9) is calculated by Shear Demand over Shear Capacity .

\( \text{ratio} = \frac{\text{Shear Demand}}{\text{Shear Capacity}} \rightarrow \) Equation 9

Flexure

Flexural isolated

Figure 3. Critical moment section of Flexure

The Flexure located at the Moment critical section in footing within perpendicular of reinforced concrete column face  (Refer to Figure 3).

\( \text{M}_{u} = \text{q}_{u} \times \left ( \frac{l_{x}}{2} – \frac{c_{x}}{2} \right ) \times l_{z} \times \left ( \frac{\frac{l_{x}}{2} – \frac{c_{x}}{2} }{2} \right ) \rightarrow \) Equation 10

where:
qu = factored soil pressure, ksf or kpa
lx = footing dimension parallel to x-axis, in or mm
lz = footing dimension parallel to z-axis, in or mm
cx = column dimension parallel to x-axis, in or mm

The Flexure Demand orMu is located at a distance of column face the (blue) hatch area indicated in Figure 3.

\( \phi\text{M}_{n} = \phi_{\text{flexure}} \times A_{s} \times f_{y} \times \left( d \times \frac{a}{2} \right) \rightarrow \) Equation 11


where:
ϕ = flexural factor
lx = footing dimension parallel to x-axis, in or mm
lz = footing dimension parallel to z-axis, in or mm
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in or mm
As = reinforcment area, in2 or mm2
a = depth of equivalent rectangular stress block, in or mm
fy = steel strength, ksi or MPa

The Flexure Capacity or ϕMn is calculated  through equation 11.

\(\text{M}_{\text{u}} \leq  \phi\text{M}_{\text{n}} \rightarrow \) Equation 12 (ACI Eq. 7.5.1.1(b))

In skyCiv , In compliance of Equation 12, the calculation two-way shear ratio (Equation 13) is calculated by Flexure Demand over Flexure Capacity .

\( \text{ratio} = \frac{\text{Flexure Demand}}{\text{Flexure Capacity}} \rightarrow \) Equation 13

Albert Pamonag Structural Engineer, Product Development


Albert Pamonag
Structural Engineer, Product Development
B.S. Civil Engineering

References

  • Taylor, A. Hamilton III, T. Nanni, A. (2015) The Reinforced concrete design handbook: a companion to ACI-318-14.  American Concrete Institute
  • McCormac, J. Brown, R. (2015) Design of Reinforced Concrete 10th Edition.
  • Building Code Requirements for Structural Concrete (ACI 318-14)
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