Structural Design of Pile Caps Using Strut and Tie Model

Structural Design of Pile Caps Using Strut and Tie Model (EC 2)

Pile caps are concrete mats that rests on piles with adequate rigidit to transfer the column loads to the piles! Piles are pro"ided as alternati"es to shallow foundations when a firm and sta#le soil to carr column load is too deep #elow the surface$ or when high lateral load is anticipated! More often than not$ pile caps are usuall so rigid that the ma%e the entire group of piles to #eha"e li%e one unit! E& '2''*2++, permits us to use strut and tie models to analse structures where nonlinear strain distri#ution e-ists (e!g! pile caps$ deep #eams and cor#els)! .n strut and tie models$ trusses are used with the following components* / Struts (concrete) / Ties (reinforcement) / &odes (intersections of struts and ties) Eurocode 2 gi"es guidance for each of these!

Design Example

 0 1++mm - 1++mm column is carring an ultimate limit state load of 2',+ %&! e are to design the pile cap using the following data3 2 4rade of concrete f c% c% 5 6+ &7mm 8% 5 1++ &7mm2 Concrete co"er 5 91mm Spacing of pile 5 ':++mm Diameter of piles 5 ;++mm

The strut and tie model is as gi"en #elow3

Solution

 0ngle of inclination of strut < 5 tan' (''++7++) 5 1+!9'+= cos < 5 +!;66 sin < 5 +!996 8orce in strut 8s 5 '+9+7sin< 5 '6:2!;+91 %& 8orce in tie 8t 5 '6:2!;+91 cos < 5 :91!'1 >&  0rea of tension steel required 0s 5 8t7+!:98% 5 (:91!'1 ? '+++) 7 (+!:9 ? 1++) 5 2+''!: mm2 Pro"ide 9@2+ A '1+ c7c (0spro" 5 2': mm2 )  0smin 5 +!'6#h7'++ 5 +!++'6 ? ++ ? '2++ 5 ',+, mm2 Since pile spacing is less than three times pile diameter$ the #ars ma #e spread uniforml across the cap! Check for Shear 

Consider the critical section for shear to #e located at 2+B of the pile diameter inside the pile cap!

Distance of this section from the column face3 a" 5 +!1(Spacing #etween piles  width of column)  +!6(pile diameter) a" 5 +!1(':++  1++)  +!6(;++) 5 ,9+ mm ength of corresponding perimeter for punching shear  u 5 2(++  ',,+) 5 ,;:+mm Perimeter of pile cap 5 2(++  29++) 5 92++mm Since the perimeter of the pile cap is less than 2u$ normal shear e-tending across the full width of the pile cap is more critical than punching shear! The contri#ution of the column load to the shear force ma #e reduced # appling a factor  5 a"72d$ where +!1d F a" F 2d Gut a little consideration will show that a"(,9+ mm) H +!1d(11+ mm)$ therefore$ ta%e a" as +!1d (11+) Therefore  5 11+ 7 2(''++) 5 +!21  5 I7#d

v 

I 5 '+9+ >&  (Self weight of pile cap72) Self weight of pile cap 5 '!61(21 ? 2!9 ? +! ? '!2) 5 :!,'1 >&  5 (+!21 ? '''!2 ? '+++)7(29++ ? ''++) 5 +!+,2 &7mm2

v 

IJd$c 5 KCJd$c!%!('++L' f c%)('76)  %'!cpN O (Imin  %'!cp)

CJd$c 5 +!':7&  5 I7ud 2 v  5 (2',+ ? '+++)7(2+++ ? ''++) 5 +!92 &7mm v 

IJd$ma- 5 +!2('  f c%721+)f c% IJd$ma- 5 +!2 ('  6+721+)6+ 5 1!2: &7mm2 This shows that the punching shear around column perimeter is o%!