# P DELTA Analysis of Pile Foundation

## General

First order analysis assumes small deflection behavior; the resulting forces and moments take no account of the secondary effects due to the deformation of the structure under load.

Second order analysis combines two effects to reach a solution: - 1st order analysis & large displacement analysis. The large deformation analysis takes full account of the effects due to the deformed shape of the structure and its members. When structures become more slender and less resistant to deformation, consideration of the 2nd order effects is a must.

## P–Delta analysis

The objective of this article is to provide engineers with a short introduction of P-Delta analysis currently available in commercially software packages.

P-Delta is a non-linear effect that occurs in every structure where elements are subject to axial load. P-Delta is actually only one of many second-order effects. It is a genuine “effect” that is associated with the magnitude of the applied axial load (P) and a displacement (delta).

There are two P-Delta effects:
• P-"BIG" delta (P-Ä) - a structure effect
• P-"little" delta (P-ä) - a member effect
The discussed model, where the soil is loosely compacted, the shaft resistance as well as the end bearing resistance of casing driven piles can be improved by the "dublex redriving" process. After driving the casing together with its shoe as deep as possible, the hole is filled by lean concrete while the casing is continuously withdrew in jerks leaving the shoe behind. Another shoe is then placed on the top of this freshly poured column of lean concrete and casing is redriven together with the new shoe through this column of concrete, thereby forcing this concrete side says and down until an acceptable set is obtained. Thereafter, the operations of placing the reinforcement, Concreting and pulling out the casing afresh are executed as in a usual driven and cast in situ pile.

Consider the pile foundation, as shown under the bridge pier in scourable cohesive soil, layout of piles in plan and the values of direct moments and lateral forces at the soffit of Pilecap, are as follows:
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NBM&CW June 2010

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