Recent content by T1m0

Tygra, the equation that you came up with is an oversimplification of the mechanical behavior of the slab (plate). The correct model for the slab is the equation for plate bending which has a mixed derivative in the differential equation for the deflection. The distributed load q in plate...

Tygra, in your original post you wrote the equations for the deflection of a beam (except the dx in the denominator should be to the fourth power not the second). The resulting units for q come out to force per unit length. Although the same symbol q is used to represent a distributed load in...

Here are two references on solving plate bending problems using finite differences. https://ir.nbu.ac.in/server/api/core/bitstreams/feef3198-3874-4ac5-a460-ce354bf657a7/content https://hrcak.srce.hr/file/328655

A slab would ordinarily modeled using plate theory which is more complex than the equations that you started with. You can find a brief overview in Wikipedia.

Juanda, you can find a fairly thorough explanation of the pressure vessel formulas in https://pkel015.connect.amazon.auckland.ac.nz/SolidMechanicsBooks/Part_I/BookSM_Part_I/07_ElasticityApplications/07_Elasticity_Applications_03_Presure_Vessels.pdf I am not aware of any analytical solutions to...

Juanda, There is a Section in Roark's book on Thin Walled pressure vessels that gives a fairly simple formula for the radial expansion of a spherical tank as a function of internal pressure. The effect of this expansion on the pressure will strongly depend on whether the fluid inside the tank...

The solution in Roark's book can be found in the chapter on Beams in the section for "Beams under simultaneous axial compression and transverse loading." The complexity of the expression depends on which edition of the book that you have. The later editions are more difficult to decipher than...

Actually, there is a fairly simple analytical solution in Roark's Formulas for Stress and Strain book; i.e., y_B=(F_y/F_x)*(k*tan(L/k)-L) where k=sqrt(E*I/F_x)

You can solve for y_B. Just crank through the algebra using the 3 boundary conditions. The third condition will give you an equation where y_B appears on both sides of the equation. By the way, I am apparently too technology challenged to get Latex to work for me. That's why the equations...

The solution of the differential equation is y=C_1*sin(k*x)+C_2*cos(k*x)+C_3*x+C_4 where k=sqrt((F_x/(E*I)), C_3=-F_y/F_x, C_4=(F_x*y_B+F_y*L)/F_x Use the three boundary conditions to solve for C_1, C_2, and y_B.

You can use the elementary beam theory equation d^2y/dx^2=-M/EI as long as the displacements are not too large (This case can be solved in closed form). How large is too large? - That tends to be problem dependent. As you indicated, the more complex expression for the beam radius of curvature...

In your cantilever beam example, you did not get the internal bending moment quite right because you assumed that it was simply a linear function of x. I suggest that you get the moment by cutting the beam at some position x and drawing a free body diagram. This will lead to the following...

I agree that Roark's book is not very useful for learning analysis techniques. If you want to ease into the subject, I suggest that you start with a basic book on Mechanics of Materials. Typically, there will be a chapter on bucking of beams where there will be a section on columns with...

In Roark's book, there should be a section on "Beams Under Simultaneous Axial and Transverse Loading." If P is the axial load and W is the transverse load at the end, then the transverse end deflection is y=W/(k*P)*(tan(kL)-kL) where k=(P/(EI))^(1/2) and L is the length of the beam.

This is a case of a beam under combined axial and transverse loading (Beam-columns). The displacement formula for your specific case can be found in Roark's Formulas for Stress and Strain. Techniques for analyzing these types of problems can be found in textbooks on Advanced Mechanics of...