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Steel Base Plate Designer to EC3's banner
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Steel Base Plate Designer to EC3

Verified by the CalcTree engineering team on August 8, 2024

This calculator designs a steel base plate for a steel I-section column in axial compression. It computes the required thickness and plan dimensions of a base plate.
All calculations are performed in accordance with BS-EN-1993-1-8:2005 Eurocode 3: Design of steel structures - Part 1-8: Design of joints, which is part of the "EC3" or "Eurocode 3" code series.


Calculation

Assumptions

Inputs

Base plate



Ned
:2 MN​

ULS design compression load


fy
:275 MPa​

Yield strength of the steel base plate


Concrete Support Properties



fck
:25 MPa​

Compressive strength of the concrete support


alpha_cc
:0.85​

Concrete coefficient for long-term effects (refer to your National Annex)


gamma_c
:1.50​

Partial factor of safety for concrete (refer to your National Annex)


Steel Column Properties



Section
:UC - 203x203x60​



h
:210mm​


b
:206mm​


tw
:9.4mm​


tf
:14.2mm​


r
:13mm​


Perimeter
:1202mm​


Area
:7686mm2​


Outputs



fjd
:14.24 MPa​

Bearing capacity of concrete support


A_req
:218 sqin​

Required minimum base plate area


c
:86 mm​

Additional bearing width


wp
:378 mm​

Required minimum base plate width


lp
:382 mm​

Required minimum base plate length


tp
:34 mm​

Required minimum thickness of base plate
Output parameters of a base plate with an I-section


Is the calculator valid, that is, do the T-stubs overlap?

Check
:OK, there is no overlap between T-stubs.​



Explanation

Steel base plates are provided beneath steel columns in order to transmit the applied design forces safely to the foundations. Since steel columns are heavily loaded and their cross-sections are typically small, applying the loads directly on the foundation could result in a punching failure. Therefore a base plate must be provided beneath the column in order to spread the column load over a larger base area.

The actual distribution of pressure beneath a base plate is quite complex. EN 1993-1-8:2005 clause 6.2.5 and 6.2.8 presents a simplified approach. It assumes a uniform distribution of pressure beneath an effective area of the base plate known as the "equivalent T-stub in compression". The dimension,

in the figure below known as the "additional bearing width", forms an effective bearing area given by

. The required check is that the applied compressive stress on this effective area does not exceed the design bearing strength of the concrete support,

.
Area of equivalent T-stub in compression, adapted from Figure 6.4 EN 1993-1-8

As per Clause 6.2.8.2, the capacity of a symmetric column base plate subject to an axial compressive force applied concentrically may be determined by adding together the capacities of the three T-stubs shown below (two T-stubs under the column flanges and one T-stub under the column web). The three T-stubs should not be overlapping.
Effective bearing area of a base plate with I-section, adapted from Figure 6.19 EN 1993-1-8

The steps for this "equivalent T-stub in compression" design method are based on a research paper from the University of Ahmadu Bello, and are as follows:

Step 1) Compute the bearing strength,

of the concrete support


fjd=βj×α×αccfckγcf_{jd} = \beta_j \times \alpha \times\dfrac{\alpha_ {cc}f_{ck}}{ \gamma_c}
Where:
  1. 
    
    is the foundation joint material coefficient, typically taken as 0.67 as per clause 6.2.5(7) in EN 1993-1-8. This calculator takes
    
    .
  2. 
    
    is a coefficient which accounts for the concrete bearing strength enhancement due the diffusion of the concentrated force within the foundation, as per clause 6.7 in BS EN 1992-1-1 (code also known as "EC2"). The value of
    
    can be calculated directly if the dimensions of the concrete foundation is known. Otherwise, usual foundation sizes relative to that of the baseplate is shown to give
    
    [source: SCIA Engineer]. This calculator conservatively takes
    
    .
  1. 
    
    is the characteristic compressive strength of the concrete support
  1. 
    
    is the concrete coefficient for long-term effects, refer to your country's National Annex.
  1. 
    
    is the partial factor of safety for concrete, refer to your country's National Annex.


💡Derivation of



The equation above is not explicitly stated in the standards. It can be derived as per the following:
  1. As per clause 6.2.5(7) in EN 1993-1-8,
    
    where
    
    is the effective area given by
    
    
  1. As per clause 6.7 in BS EN 1992-1-1,
    
    where
    
    is a coefficient given by
    
    
  2. As per clause 3.1.6 in BS EN 1992-1-1,
    
    
Putting all the equations together:

fjd=βj×[Ac0×[αcc×fck]/γc×α]Ac0=βj×α×αccfckγcf_{jd}=\dfrac{\beta_{j}\times [A_{c0}\times [\alpha_{cc}\times f_{ck}]/\gamma_c\times \alpha ]}{A_{c0}}\\ \hspace{0.55cm}= \beta_j \times \alpha \times\dfrac{\alpha_ {cc}f_{ck}}{ \gamma_c}


Step 2) Find the required area of the base plate,




Areq=NEdfjdA_{req} =\dfrac{N_{Ed}}{f_{jd}}
Where:
  1. 
    
    is the ULS design compression load from the column on the baseplate
  2. 
    
    is the bearing strength of the concrete support

Step 3) Find the additional bearing width,


The additional bearing width,

is obtained by equating the effective area,

to the required rectangular area,

. The equation for

is the sum of the effective areas of the three T-stubs (assuming no overlap), and is found using geometry.

Aeff=4c2+Pcol×c+Acol→Aeff=Areq=NEdfjd→4c2+Pcol×c+Acol−NEdfjd=0Solve for c.A_{eff}=4c^ {2}+ P_{col }\times c + A_{col}\\\rightarrow A_{eff}=A_{req} =\dfrac{N_{Ed}}{f_{jd}} \\\rightarrow 4c^ {2}+ P_{col }\times c + A_{col}-\dfrac{N_{Ed}}{f_{jd}} =0\\\text{Solve for }c.


Step 4) Find the required base plate plan dimensions

Required baseplate width,

and length,

is given by:

wp=b+2clp=h+2cw_p=b+2c\\l_p=h+2c

Note, as per EN 1993-1-8:2005 Section 6.2.5(5)&(6), if the baseplate has larger plan dimensions then required to fit

, the additional projection beyond

is neglected from the effective bearing area.


Step 5) Calculate the required base plate thickness,


Re-arranging the equation in clause 6.2.5(4) EN 1993-1-8 gives the required baseplate thickness:

tp=c×3×fjd×γM0fyt_{p}=c\times \sqrt{ \dfrac{3 \times f_{jd}\times\gamma_{M0}} {f_y }}
Where:
  1. 
    
    is the yield strength of the T-stub (i.e. the steel baseplate)
  1. 
    
    is the bearing strength of the concrete support
  2. 
    
    is the partial factor for resistance of cross-sections whatever the class is as per EN 1993-1-1. This calculator takes the code recommended value of
    
    .


Acknowledgements

This calculation was built in collaboration with Kamaludeen Samaila. Learn more.

Related Resources

  1. Bolt Group Calculator to AS 4100
  2. Steel Base Plate Designer to AISC 360
  3. Steel Section Designer to EC3
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