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This steel baseplate calculator checks against concrete crushing from a column in compression and provides the minimum required baseplate thickness. There are three types of calculations for different columns types: wide flange, tube and pipe.
This calculation has been written in accordance with:
  1. AISC 360-05 Specification of Structural Steel Buildings - Allowable Stress Design and Plastic Design
  2. AISC Steel Construction Manual 16th Edition
Note this version of the code has been superseded by AISC 360-22, though the calculation remains valid. The main difference is the value for safety factor for compression, Ωc, which has a value of 2.50 in AISC 360-05 and 2.31 in AISC 360-22. The value Ωc is available for user input in this calculator.


Calculation

Assumptions

  1. Column is loaded axially only, i.e. no bending or shear is considered
  2. Column load is distributed to the concrete foundation as a uniform bearing pressure

Wide Flange

Wide flange column base plate design variables


Inputs



Pa
:200kips​



Fy
:60ksi​



fc'
:3ksi​



Column designation
:W10X26​



N
:16in​



B
:16in​



A2
:1156sqin​



Ωc
:2.31​


Output



USE
:16 x 16, 1-1/4in thick plate​

Bearing check:


Pp/Ωc
:565.1948051948044kips​



Check
:> 200kips Satisfactory​

Minimum required base plate thickness:


t, minimum
:1.185240268363339in​



Design Variables



d
:10.3in​



b
:5.77in​




m
:3.1075in​



n
:5.692in​

Note, if m and/or n is a negative value make your baseplate bigger!


n'
:1.9272876017865106in​



X
:0.3257415134193303​



λ
:0.6267942729282144​


Tube

Tube column base plate design variables


Inputs



Pa
:200kips​



Fy
:60ksi​



fc'
:3ksi​



Column designation
:HSS20X12X5/8​



N
:16in​



B
:16in​



A2
:1156sqin​



Ωc
:2.31​


Output



USE
:16 x 16, 3/4in thick plate​

Bearing check:


Pp/Ωc (1)
:565.1948051948044kips​



Check
:> 200kips Satisfactory​

Minimum required base plate thickness:


t, minimum
:0.6866924334930261in​



Design Variables



d
:20.0in​



b (1)
:20.0in​




m
:-1.5in​



n
:-1.5in​

Note, if m and/or n is a negative value make your baseplate bigger!


n'
:5.0in​



X
:0.3538602941176478​



λ
:0.6595545959368446​


Pipe

Pipe column base plate design variables


Inputs



Pa
:200kips​



Fy
:60ksi​



fc'
:3​



Column designation
:HSS2.375X0.250​



N
:16in​



B
:16in​



A2
:1156sqin​



Ωc
:2.31​


Output



USE
:16 x 16, 1-1/2in thick plate​

Bearing check:


Pp/Ωc (1)
:565.1948051948044kips​



Check
:> 200kips Satisfactory​

Minimum required base plate thickness:


t, minimum
:1.4680154413143955in​



Design Variables



d
:2.375in​



b
:2.375in​




m
:7.05in​



n
:7.05in​

Note, if m and/or n is a negative value make your baseplate bigger!


n'
:0.59375in​



X
:0.3538602941176478​



λ
:0.6595545959368446​



Explanation

What are base plates?

Steel base plate (image: Miguel Cervera)

Steel base plates are used to distribute the load of a column or other structural member to a concrete foundation and provide a connection for the anchor bolts between the column and concrete foundation. They are typically made of ASTM A36 steel, which is a mild steel with good weldability and formability. Base plates are also available in higher strength steels, such as ASTM A572 Grade 50, for applications where higher loads are expected.
Typical column base for axial compressive loads [1]

Generally, a column base plate is made with a plate and a minimum of four anchor rods.
Levelling nuts and washers [1]


Why are base plates used?
  1. They can distribute loads over a large area. Concrete foundations are typically weaker than the steel column, but with the load distribution it will prevent concrete crushing.
  2. They can be used to level columns. This helps ensure that the column is vertical for the overall stability of the structure.
  3. They can be used to provide clearance between the column and foundation. This allows for drainages and prevents the steel column from corrosion.

Concrete Crushing Limit State

The column axial force is distributed from the column end to the column base in direct bearing. AISC 360-16 J8 outlines that in the absence of code regulations the allowable bearing strength for the limit state of concrete crushing can be taken with the safety factor of compression, Ωc = 2.31. The allowable bearing strength, Pp/Ωc is:

PpΩc=fc′A1Ωcmin⁡[0.85MAX⁡(A2A1,1),1.7]where:Pp=nominal bearing strength of concreteΩc=safety factor for compression=2.31  (ASD)fc′=specified minimum compressive strength of concreteA1=area of steel concentrically bearing on a concrete supportA2=maximum area of the portion of the supporting surface that is geometrically similar to and concentric with the loaded area\dfrac{P_p}{\Omega_c}=\dfrac{f_c^{\prime} A_1}{\Omega_c} \operatorname{min}\left[0.85\operatorname{MAX}\left(\sqrt{\dfrac{A_2}{A_1}}, 1\right), 1.7\right]\\\text{}\\\text{where:}\\P_p=\text{nominal\ bearing\ strength\ of\ concrete}\\\Omega_c=\text{safety\ factor\ for\ compression}=2.31\;\text{(ASD)}\\f'_c=\text{specified\ minimum\ compressive\ strength\ of\ concrete}\\A_1=\text{area\ of\ steel\ concentrically\ bearing\ on\ a\ concrete\ support}\\\\A_2=\text{maximum\ area\ of\ the\ portion\ of\ the\ supporting\ surface\ that\ is\ geometrically\ similar\ to\ and\ concentric\ with\ the\ loaded\ area}

Base Plate Design

The design dimensions of the base plate m, n and n'λ are to determine the critical base plate cantilever dimension, l which is used to calculate the minimum base plate thickness tmin.
The critical base plate cantilever dimension, l, determines the critical bending strength of the baseplate. The required strength (column axial force), Pa, is distributed from the column end to the column base plate in direct bearing. The column base plate is then assumed to distribute the column axial force to the concrete or masonry as a uniform bearing pressure by cantilevered bending of the plate.
The factored dimensions bf and d are the minimum required dimensions, for width and depth respectively, for the base plate in order to prevent yielding of the baseplate or buckling of the anchor bolts.
The minimum required thickness of the base plate, tmin is outlined in AISC Steel Construction Manual 14th ed. 14-6 as:

tmin=l3.33PaFyBNwhere:l=critical base plate cantilever dimension=max⁡(m,n, n′λ)Pa=compression axial loadFy=yield strengthB=base plate widthN=base plare deptht_{min}=l\sqrt{\dfrac{3.33P_a}{F_yBN}}\\\text{}\\\text{where:}\\l=\text{critical\ base\ plate\ cantilever\ dimension}=\operatorname{max}(m,n,\ n'\lambda)\\P_a=\text{compression\ axial\ load}\\F_y=\text{yield\ strength}\\B=\text{base\ plate\ width}\\N=\text{base\ plare\ depth}
Wide flange column base plate design variables

Tube column base plate design variables

Pipe column base plate design variables


The design variable dimensions are outlined in AISC Steel Construction Manual 14th ed 14-5 as the following:

n′=db4X=min⁡[(4db(d+b)2)ΩcPaPp,1]λ=min⁡(2X1+1−X,1)where:N=base plate depthB=base plate widthd=column depthb=column widthΩc=safety factor for compressionPa=compression axial loadPp=norminal bearing strength of concreten^{\prime}=\dfrac{\sqrt{d b}}{4} \\ X=\operatorname{min}\left[\left(\dfrac{4 d b}{\left(d+b\right)^2}\right) \frac{\Omega_c P_a}{P_p}, 1\right]\\\lambda=\operatorname{min}\left(\dfrac{2 \sqrt{X}}{1+\sqrt{1-X}},1\right)\\\text{}\\\text{where:}\\N=\text{base\ plate\ depth}\\B=\text{base\ plate\ width}\\d=\text{column\ depth}\\b=\text{column\ width}\\\Omega_c=\text{safety\ factor\ for\ compression}\\P_a=\text{compression\ axial\ load}\\P_p=\text{norminal\ bearing\ strength\ of\ concrete}
Note: λ can be taken conservatively as 1
Wide flange

m=N−0.95d2n=B−0.8b2m=\dfrac{N-0.95 d}{2} \\ n=\dfrac{B-0.8 b}{2}
Tube

m=N−0.95d2n=B−0.95b2m=\dfrac{N-0.95 d}{2} \\ n=\dfrac{B-0.95 b}{2}
Pipe

m=N−0.8d2n=B−0.8d2m=\dfrac{N-0.8 d}{2} \\ n=\dfrac{B-0.8 d}{2}

References

[1] American Institute of Steel Construction. (2022). Specification for structural steel buildings (AISC 360-22). Chicago, IL.
[2] American Institute of Steel Construction. (2011). Steel Construction Manual (14th edition). Chicago, IL.

Related Resources

  1. Rectangular Spread Footing Design to ACI
  2. Steel Beam and Column Designer to AISC
  3. Steel Beam and Column Designer to AS4100
  4. Slab Thickness Calculator to ACI 360R-10