Author: Rajesh Naik
Rajesh Naik has over 30 years of experience as a piping engineer in the oil and gas (onshore and offshore), petroleum and petrochemical industry. The author has been involved in FEED, Detailed Engineering and Construction Engineering phases of the project and has experience with Consulting Organizations, EPC Contractors and Client Organizations in PMC role.
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Young's Modulus

E (Young's Modulus) relates the amount of strain (stretching) to the amount of stress

(loading). It is defined as:

E = S/E


The value of E changes with material and temperature. The stress and strain are

measured experimentally. E is calculated and is tabulated in the piping code.


E = 30,000,000 P.S.I. for Cold Steel


Normally designed anchors cannot stand large forces because the structure would bend first, and the anchor would not be effective. Equipment shells would dimple before they would act as anchors. Expansions are absorbed by bending the piping system rather than compressing it.

Thermal Force between Two Anchors

Free Expansion △ = eL

The force required to prevent the pipe from expanding is the same as the force required to stretch it an equal amount.

Since S=P/A and E=S/€ and € = △/12L (feet converted to inches) 

To find P (the Force),


P=SA = E ∈ A = E(△/12L)A = E(eL/12L)A

p = eAE/12



For a 6” Sch. 40 Pipe at 300°F

P = .0182 x 5.58sq in. x 30,000,000 psi / 12 

P = 253,800#


Nomograph A:

See Figure #1-16, Nomograph A 

This Chart is based on formula (modified) P= => I2EI△/L3

This formula will not be used in the lesson. 

Moment of inertia is the stiffness of object being bent based on its cross-sectional shape. This formula shows force is directly proportional to the deflection. Force is inversely proportional to the bending leg cubed.

Size and schedule relates to moment of inertia. Lengths to be added are approximate. The force found in this way can differ greatly from a computer output, but is good enough for piping study purposes.

The total free expansion between the two restraints (guide and anchor) is trying to grow outwards in either direction simultaneously since it can't actually move at either end.