The following article will guide you about how to design base plates used in steel structures.
Column Base:
While a foundation is necessary for a column to distribute the column load on sufficient area of the soil so that the bearing capacity of the soil is not exceeded, it is also equally important that the column load should be applied on sufficient area of the concrete foundation so that the bearing strength of concrete is not exceeded. A steel base plate is therefore provided to distribute the column load on sufficient area of concrete foundation.
Base plates used may be of the following types:
(i) Slab Base:
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A slab base plate is provided when the column is to stand on an independent concrete foundation. The bearing end is machined so as to provide full contact with the base plate so that-the column load is transmitted to the base plate by bearing. In order to prevent any possible dislocation of the column at the stage of erection, sometimes secondary joint is also provided connecting the column (web) and the base plate.
Under the action of the downward load exerted by the column on the base plate, and the upward reaction exerted by the concrete foundation, the base plate is subjected to bending in two principal directions. Considering this the I.S. 800 code has given the following specification.
The minimum thickness ts of the rectangular slab bases, supporting columns under axial compression shall be-
where,
w = uniform pressure from below on the slab base under the factored axial compressive load
a, b = Larger and smaller projections respectively beyond the rectangle circumscribing the column, and
tƒ = Flange thickness of the column.
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Design Procedure:
Let P = Factored axial load on the column area of slab base plate required
A = Factored load on the column/Design bearing strength of concrete
Design bearing strength of concrete = 0.45 ƒck
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where, ƒck = characteristic strength of concrete
The plan dimensions of the slab base plate may now be selected to provide the above area and also so that the projections a and b beyond the rectangle circumscribing the column area nearly equal (Fig. 7.59).
The plan dimensions L and B of the base plate are such that-
After selecting convenient dimensions L and B of the base plate find the exact values of a and b (which are nearly equal), a being the greater of the two.
Now find the upward pressure intensity on the base plate
P = P/(L × B)
Now find the thickness of the base plate using the specification-
The base plate is fitted to the concrete foundation with two or four 20 mm diameter holding down bolts.
When the column load is axial and the column end and the base plate are machined and the column is not subjected to bending moment, nominal connections are made connecting the column flanges and the base plate with cleat angles say 60 mm × 60 mm × 8 mm. Where the column end is not machined the connection is designed to transmit the column load to the base plate through welded connection.
Sometimes a base plate of dimensions greater than the requirement may have been provided. In such cases the I.S. 800 code has made the following specification.
If the size of the base plate is larger than that required to limit the bearing pressure on the base support, an equal projection c of the base plate beyond the face of the column and gusset may be taken as effective in transferring the column load as given in Fig. 7.60, such that the bearing pressure on the effective area does not exceed the bearing capacity of concrete base.
(ii) Gusseted Base:
Gusseted base plates are used for columns carrying heavy loads and loads accompanied by moments. In this case fastenings are used to connect the base plate and the column in the form vertical gusset plates and gusset angles. The usual arrangement consists of a base plate, two gusset plates one over each flange of the column and two angles.
The gusseted base plate may be designed as follows:
(i) Divide the factored load on the column by the design bearing strength of concrete and find the area of the base plate required.
(ii) Choose a thickness of gusset plate (16 mm) and gusset angle (say 150 x 115 x 15). The vertical leg of the angle must have a length to accommodate two bolts. To accommodate all these elements the width of the base plate is determined.
Length of the base plate = Area of base plate required/Width of the base plate
(iii) Bearing stress on base plate-
= w = Column load/Actual area of base plate
(iv) Let b = distance between the gussets
c = cantilevering projection of the base plate
Cantilever moment per unit width = M1 = wc2/2
Thickness r required for this moment is calculated.
B.M. at the Centre:
The part of the base plate between the gusset plates bends in two principal directions. Considering two way slab action the B.M. at the centre may be taken as-
Thickness required for this moment is calculated.
The greater of the thicknesses determined from the above two consideration is adopted,
(v) Connections are designed for 50% of the column load.
If P = Factored load on the column
Gusseted Welded Base Plate:
In this case the base plate may be designed as follows:
(i) Divide the factored column load by the design bearing strength of concrete and find the area of the base plate.
Select a convenient width of the base plate.
Width of base plate = Depth of the column section + 2 (thickness of gusset plate) + 80 mm to 100 mm
Length of the base plate = Area of base plate required/Width of the base plate
Actual bearing stress on the base plate
= w = column load/Actual area of the base plate
(ii) Cantilever moment for a 1 mm wide strip
= M1 = wa2/2
Span moment for a 1 mm wide strip (considering two way bending)
M2 = 0.2w[(b2/8) – (a2/2)]
Determine the thickness of the base plate required corresponding to the greater of the above bending moments.
Connections:
Load transmitted to one gusset plate = 1/4 (load on the column)
Length of weld on one gusset plate to connect with the column = Load on one gusset plate/Strength of weld per mm length
The height of the gusset plate may be selected to accommodate the weld. The height of the gusset plate may be reduced to 100 mm at the ends. Similarly, provide also weld connection between the gusset plate and the base plate.
Eccentrically Loaded Base Plate:
When a column carries a load eccentrically or when the column carries an axial load accompanied by a moment the pressure distribution below the base plate will not be uniform.
Suppose a column carries a factored load P at an eccentricity e. The moment due to the eccentricity = M = Pe. Alternatively if a column carries an axial load P and is subjected to a moment M we may consider as though the load P is at an eccentricity e given by-
e = M/P
Let B be the width and L the length of the base plate (Fig. 7.72). When the column carries the load P at an eccentricity e the extreme pressure intensity on the base plate is given by P/A [1 ± 6e/L] when the eccentricity e is less than or equal to 1/6 [A = area of base plate = BL]
Length of the base plate = L = Depth of the column section 2 times the cantilever projection of the plate parallel to the length.
The cantilever projection of the plate beyond the column face parallel to the length may be chosen from 100 mm to 150 mm.
We come across the following three cases:
Case (i). When the Eccentricity e < 1/6:
For this case we know the extreme pressure intensifies on the base plate are-
The width B of the base plate may be determined corresponding to the condition-
Generally the width B is determined corresponding to e = L/6
After finding B, we can determine the cantilever moment M for a 1 mm wide strip due to upward pressure on the base plate.
Equating the moment capacity to the cantilever moment-
Case (ii) When the Eccentricity lies between 1/6 and 1/3:
In this case the pressure distribution diagram under the base plate is a triangle. Let L be the length of the base plate. For the condition, that the line of action of the upward reaction and the line of action of the load P to coincide the length of the pressure diagram below the base plate-
= x = 3[(1/2) – e]
Let the maximum pressure intensity pmax reach the design bearing strength of concrete. Let B be the width of the base plate. Equating the upward and downward forces-
1/2pmaxLB = P
We can find B from the above equation. Now we can easily calculate the maximum bending moment for the base plate and hence determine the thickness of the base plate.
