Maximum bending moment is M = F a Second moment of area for cross-section of steel pipe: Ie = pi (D^4 - d^4) / 64 Ie = pi (120^4 - 117^4) / 64 = 980338mm^4 Second moment of area for cross-section of refractory lining: Ii = pi (d^4 - t^4) / 64 Ii = pi (117^4 - 76^4) / 64 = 7560760mm^4 where: D =120mm , d =117mm, t =76mm. Now I'm going to split forces and corresponding moments in two parts: - Fe, Me - force and moment carried by steel - Fi, Mi - force and moment carried by refractory lining so that net force and moment are: F = Fe+Fi M = Me + Mi First, I'm going to find force Fe from maximum allowable bending stress in steel pipe se=DMe/(2 Ie) where Me - moment carried by steel pipe, Me=Fe a se=D Fe a /(2 Ie) Fe = 2 Ie se / (D a) Fe = 2 * 980338 * 183.3 / (120 * 400) Fe = 7487.3 N Now I'm going to find deflections for both pipes. Relation between deformation y, moment M, second moment of area I and Young's modulus E is: y'' = - M / B Integration yields: ymax = f = F L^3 a [3/4 - (a/L)^2] / ( 6 E I L) where L = 1200mm a = 400mm For external pipe (steel) fe = Fe L^3 a [3/4 - (a/L)^2] / ( 6 Ee Ie L) and for internal pipe (refractory lining): fi = Fi L^3 a [3/4 - (a/L)^2] / ( 6 Ei Ii L) These deflections are equal, f = fi = fe, and common deflection is f = fi = fe = 7487.3 * 1200^3 * 400 * [3/4 - (400/1200)^2] / (6 * 2.12*10^5 * 980338 * 1200) f = 2.21 mm and it is located in the middle of the span. Force carried by refractory lining can be found as force required to cause deflection fi = f of interior pipe. It can be calculated either by means of full formula for deflection of inner pipe fi (given above), or by ratio of forces like this: Fi / Fe = (Ei Ii) / (Ee Ie) Fi / Fe = (0.145*10^5 * 7560760) / (2.12*10^5 * 980338) Fi / Fe = 0.5275 In both cases, result is: Fi = 3949.6 N Maximum net force: F = Fe + Fi = 7487.3 + 3949.6 = 11436.9 N Maximum corresponding moments are: Me = Fe a = 7487.3 * 400 = 2994.92 Nm Mi = Fi a = 3949.6 * 400 = 1579.84 Nm Maximum bending moment: M =a F = 0.4 * 11436.9 = 4574.76 Nm Bending stress in interior pipe: si=d Mi/(2 Ii)= 117 * 1579840 / (2*7560760) = 12.2 N/mm^2 which is reasonably low value, so refractory lining probably won't brake if load is static. Edit - Answer to Oil Field Trash: Off course, especially if it's ceramic or similar brittle material. If this is "for real" I would either: a) calculate as if it's steel that bears all the load. b) try to unburden refractory lining, perhaps by coaxial shield or lattice around the pipe, or maybe bracing, depending on situation.
SAGE
2008-06-15 14:05:27 UTC
Well, a steel pipe with a fixed end with a lateral force placed at the top, the moment is the force times the length with will be 200 x height of the lateral force on pipe. This will give the maximum moment happening at the base of the pipe. Say for example, 200 lbs time 40 inches will be 8000 lb-in but there is something else to be considered when doing this. If you are building a wind tower then likely this pipe will have axial force. That has to be considered for stability of the column which is what this pipe will be subjected to. ASD (allowable stress design) and LRFD (Load Resistance Factor Design) stipulates that a unity condition in which the stresses in the pipe must be under the unity of one which is the actual stresses due to axial and bending moment along the x and y axis be divided by the strength of the pipe under those axial and actual bending stresses along the axis. Also, the stresses in the pipe are calulated using P/A (P=axial forces)/ (Area of pipe) and MC/I. M=Moment, c=distance from the center of gravity of the area to the outer most portion of the material, and I is the moment of inertia. 3.14 x diameter to the 4th power divided by 64. YOu have to do the other and the inner diameters and take the difference between the outer and the inner. The actual strength of the a pipe can be calculated if you have an ASD manual or a LRFD manual so there will be a little research involved. I do not have my books with me but this should get you started. Using the equations above, the stresses cannot exceed 2/3 of 60, 000 which is 40,000 psi. This is to allow for safety margin for the structural member. Also, since the pipe is subjected to lateral force, moment at the base will develop and you have to handle the moment transfer into the soil which can lead to a big foundation. If the wind tower is not too high then maybe is will not be a problem but if it is kind of big, consider foundation design. Since you are actually capturing wind, foundation design should be a consideration.
ⓘ
This content was originally posted on Y! Answers, a Q&A website that shut down in 2021.