8.3 Design of Base Plate for Thickness

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Gary Powell
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1 8.3 Design o Base Plate or Thickness Design o base plate or thickness (Elastic Design) Upto this point, the chie concern has been about the concrete oundation, and methods o design have been proposed or arriving at a base plate area that will keep the permissible stress in the support within the speciication. The base plate itsel is subject to shear and moment. It is in eect an overhanging beam and must be analysed as such. Furthermore, since the load rom an H-shaped Column is distributed dierently along its two axes the base plate must be analysed in two directions Shear and bending moment about the X - axis: Reerring to the igure 8.4 is the upward load rom the oundation is P / H N / mm along the Y axis. The share o the total load P brought to the top o the base plate by each lange is assumed to be concentrate at the mid-thickness and hence the length o overhang or cantilever is (H - d + t ) / 2. As may be noted rom the shear diagram. The point o maximum shear is also at the midthickness o the column lange and is equal to load per mm multiplied by the overhang. Thereore the maximum total shear V in the base plate along a line parallel with the axis and splitting the column lange is V x = ( + ) P H d t 2H In plotting that portion o the shear diagram beneath the column, the net upward pressure per mm must be used or P/H - Pt w /A, in which ' A ' represents the cross sectional area o the column.

2 I there are no wind or other horizontal loads the maximum bending moment in this direction M x is at the mid thickness o the column lange and is equal to the area o the shear diagram between that point and that let end P Mx = H d+ t 8H ( ) 2 Ordinates or plotting the remainder o the moment diagram and ound by the usual method o taking the algebraic sum o the shear area to the let. To get the required thickness t as governed by bending moment about the X-axis the rectangular beam ormula will apply t x = 6M Bσ bs σbs - Permissible bending steal o the plate

3 Fig 8.4

4 8.3.2 Design o base plate or thickness (Limit State Method) The required plate thickness, t reg d, is to be determined rom the limit state o yield line ormation along the most severely stressed section. A yield line develops when the cross section moment capacity is equal to its plastic moment capacity. Depending on the size o the column relative to the plate and magnitude o the actored axial load, yield line can orm in various patterns on the plate. Figure 8.6 shows three model o plate ailure in axial loaded plates. I the plate is large compared to the column, yield lines are assumed to orm around the perimeter o the eective load bearing area (the cross-hatched area) as shown in the igure 8.6a. I the plate is small and the column actored load is light, yield lines are assumed to orm around the inner perimeter o the I-shaped area as shown in igure 8.6b. I the plate is small and the column actor is heavy, yield lines are assumed to orm around the inner edge o the column langes and both side o the column web as shown in igure 8.6c.

5 Fig 8.6 Failure models or centrally loaded column base plate The ollowing equation can be used to calculate the required plate thickness t req'd = l 2P u 0.90F BN y

6 Where l is the larger o m, n and ln' given by m = n = n' = and ( N 0.95d) ( B 0.80b ) db X λ = 1+ 1 X 1 in which X 4db p u = 2 ( d+ b ) φ cpp Design base plate Thickness (IS: 800: Drat) Column and base plate connections - Where the end o the column is connected directly to the base plate by means o ull penetration butt welds, the connection shall be deemed to transmit to the base all the orces and moments to which the column is subjected. Slab Bases - Columns with bases need not be provided with gussets, but suicient astenings shall be provided to retain the parts securely in place and to resist all moments and orces, other than direct compression, including those arising during transit, unloading and erection.

7 The minimum thickness, t s o the rectangular slab bases, supporting columns under axial compression shall be 2 2 ( ) t = 2.5w a 0.3b γ / > t s m0 y Where w = uniorm pressure rom below on the slab base under the actored load axial compression a, b = larger and smaller projection o the slab base beyond the rectangle circumscribing the column, respectively t = lange thickness o compression member When the slab does not distribute the column load uniormly, due to eccentricity o the load etc, special calculation shall be made to show that the base is adequate to resist the moment due to the non-uniorm pressure rom below. The cap or base plate lateral dimension in any degree shall not be less than 1.5(d o + 75) mm in width or diameter, where d o is the nominal diameter o the pipe column or the dimension o the column in that direction. Bases or bearing upon concrete or masonary need not be machined on the underside. In cases where the cap or base is illet welded directly to the end o the column without boring and shouldering, the contact suraces shall be machined to give a perect bearing and the welding shall be suicient to transmit the orces as required in slab bases.where ull strength butt welds are provided, machining o contact suraces is not required.

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