What Does
Longitudinal Stress Mean?
Longitudinal stress is defined as the stress produced when a pipe is subjected to internal pressure. The direction of the longitudinal stress in a pipe is parallel to the longitudinal axis of its centerline axis, which means that the stress acts in the direction of the pipe’s length. Longitudinal stresses are classed as normal stresses and are tensile.
Closure of the ends of thinwalled pipes and the resulting buildup of internal fluid pressure induces the development of three types of mutually perpendicular stresses. In addition to longitudinal stress, circumferential or hoop stress and radial stress also occur, although the latter is minor compared to the others.
Longitudinal stress is also known as axial stress.
L

Longitudinal Stress


Hoop Stress

r

Radial Stress

L

Cylinder Length

d

Cylinder Diameter

t

Cylinder Thickness

P

Internal Pressure

Figure 1: Three Types of Stresses Induced in a Pipe Subjected to Internal Pressure (source)
Trenchlesspedia Explains Longitudinal Stress
It is essential to understand and evaluate longitudinal stresses when designing a pipe. The buildup of stresses in a pipe when internal pressure is applied can result in its failure. In these cases, the least invasive and most efficient methods are used during repair or replacement. Trenchless operations such as sliplining, pipe bursting, foldandformed pipe, and curedinplace pipe (CIPP) are useful in rehabilitating and replacing damaged pipes.
Calculation of Longitudinal Stress
When evaluating longitudinal stresses, there are two main forces:

Bursting Force – This is the force created due to the liquid’s internal pressure in a pipe, which damages the pipe through bursting.

Resisting Force – When the pipe is subjected to internal pressure, forces counteract the failure. This force is known as the resisting force.
If the bursting force exceeds the resisting force, then the pipe will be prone to failure. In calculating the longitudinal stress of a pipe, it is considered to be in equilibrium. Under equilibrium, the bursting force equates to the resisting force.
L

Longitudinal Stress

p

Pressure

d

Cylinder Diameter

t

Cylinder Thickness

Figure 2: Longitudinal Stress in a Cylinder (source)
As per Figure 2, the longitudinal stress is found as follows:
Bursting Force, FB=Pressure x Area=p×4×d2
Resisting Force, FR=Resisting Area×Longitudinal Stress= πdt ×L
FB=FR
p×4d2=πdt× L
∴Longitudinal Stress, L=pd4t
The Relationship between Longitudinal Stress and Circumferential (Hoop) Stress
Determination of stresses in a thinwalled pipe focuses on the two principal stresses that a pipe of this nature would be exposed to, longitudinal and circumferential. Circumferential stress acts along the pipe’s circumference, with failure tending to split the pipe into two halves. The longitudinal stress in a pipe is smaller than the circumferential stress. The formula for circumferential stress demonstrates this.

Circumferential Stress

p

Pressure

d

Cylinder Diameter

l

Cylinder Length

t

Cylinder Thickness

Figure 3: Parameters for Determining Circumferential Stress in a Cylinder (source)
Bursting Force, FB=Pressure x Area=p×d×l
Resisting Force, FR=Resisting Area×Circumferential Stress= 2tl ×
FB=FR
pdL=2tl×
∴Circumferential Stress, =pd2t
Comparing both formulas shows that the circumferential stress in a pipe under equilibrium is twice that of the longitudinal stress.