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# Plastic shear resistance of steel pipes

## Plastic shear resistance of steel pipes

(OP)
Any reference on how to derive the plastic shear resistance of a steel pipe given by the expression'
Vp = 4rt(Fy/sqrt(3))where Fy/sqrt(3)is the Von Mises yield criterion

### RE: Plastic shear resistance of steel pipes

It is just the useful component of the differential area following the shear axis along the circumference, each semicircumference gives Dt=2rt, hence for all 4rt by the shear strength.

### RE: Plastic shear resistance of steel pipes

(OP)
But my calculation indicates (pi)rt(Fy/sqrt(3)), that is,
3.14rt(Fy/sqrt(3)), not 4rt(Fy/sqrt(3))

Why I'm geting this difference? 3.14 instead of 4?

### RE: Plastic shear resistance of steel pipes

because you are having some error in the setup of your equation.

for half circumference on positive y halfspace

alfa(x)=acos((r-x)/r)

useful component of the area (its component along shear, here along x)

= t·integral between 0 and 2r of

( r·sin(alfa(x))· (d(alfa(x)/dx)· dx)

= 2rt

twice that 4rt

### RE: Plastic shear resistance of steel pipes

Other thing is that the AISC is the sole interpretation of the correct evaluation of the capacity in shear of the pipes. I think it is a smart evaluation because it acknowledges efficience to shear at midheight of the pipe section where the curve deviates less from the shear action, leaving free atop and bottom (by not counting the contribution to resist shear action of the pipe elements) to engage the tensile and compressive forces deriving from moment action.

So for a flexure setup looks quite adequate. For beamcolumn maybe the concurrence of compressive or tensile forces at the center of the section should be studied in interaction. Not looking any code, just thinking.

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