Longitudinal stress 2

[B.L.Smith]

Hi
Is there longitudinal stress in a pipe when it anchored between 5 supports? Or longitudinal stress is only for a unrestrained pipe or pipe with closure at the end of the pipe?

 

[racookpe1978]

Yes.

And yes.

(If the pipe is pressurized, it will have axial and longitudinal stress. If it is anchored and pressurized, it will have additional longitudinal and axial stresses at the support/restraint points. If it is anchored, pressurized, and heated/cooled, it will have additional longitudinal and axial (hoop) stresses at each support/restraint point.)

Now, about how much stress is at each point and in what direction?

Depends on info you have not yet provided: how much temperature change, how much pressure change, how many bends are in the "5-support" scenario: if there are none - then there will much greater stress, how long the pipe is, what friction/wear-and-tear is assumed over life in the "sliding supports", etc. In some cases, the is very little added stress. In others, the pipe fails.

 

[BigInch]

All pipes are closed and have an "end cap" pressure acting on the cross-sectional area of flow. This is a tension load and tends to stretch the pipe longitudinally. If taking a free body diagram of a segment of pipe, the "virtual end cap load" at one end, say the inlet end, = P_i * A_f and the "virtual end cap load" at the outlet end = P_o * A_f. If P_i <> P_o, then you have some fluid flow and the difference is due to friction of the fluid on the inside pipe walls. If you anchor the segment, that force is dumped into the anchor, as is the force from the next segment, hence the anchor's net load is the difference of end cap loads between one segment and another.

The Poisson component (longitudinal stress) due to hoop stress at any point (tension) is = [&nu;] * S_h, where the hoop stress is calculated using the pressure at the point of interest. [&nu;] is 0.3 for steel pipe. This potential stress is 90[&deg;] away from the hoop stress vector and in the axial direction of the pipe, and therefore makes the pipe want to shorten in that same direction. If you do not anchor each end, the pipe is free to contract, thus no stress is created. If you anchor each end, longitudinal tension stress is created.

Thermal stresses can be created with a temperature differential between installation temperature and operating temperature. If the pipe heats up, it expands in all directions. Normally only the longitudinal direction is of interest in pipe stress. If you are heating and shrinking a hub on an axle, then you are interested in the radial expansion. Trying to stop longitudinal expansion will create a compressive stress. Allowing the pipe to expand will not realize this temperature stress. Cooling would cause the opposite effect and create a tension load, but only if the pipe was restrained from contracting axially.

There can also be longitudinal components of bending stress, greatest in the outermost fibers located on the pipe OD in the plane of bending.

Torsional loads can cause torsional stresses, appearing in the pipe wall flowing around in the direction of the pipe wall, adding to hoop stress.

Shear loads also cause shear stresses, again adding in the direction of the hoop stress.

Internal pressure, in addition to hoop stress and possible Possion longitudinal stress, create a radial stress in the pipe wall, acting in the third dimension, parallel to the radius of the pipe. As would external pressure cause radial stress inward, if the pipe is placed under water, or in soil, under a road, etc.

Von Mises combined stress formula can be used to find the greatest shear stress due to all the above acting in combination.

From "BigInch's Extremely simple theory of everything."

 

[BigInch]

forgot: Shear stresses are greatest at the neutral axis.

From "BigInch's Extremely simple theory of everything."