(Matlab) beam deflection solution using symbolic simultaneous equations

In summary, to solve your simultaneous equations for the deflection at B and C, you can use Matlab's symbolic equation solver by using the command "solve" and plugging in your system of equations.
  • #1
yecko
Gold Member
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I have tried to searched for functions online and apply it, but still it does not work well.
May I ask how can I solve symbolic simultaneous equations with Matlab? Or is there anything went wrong with my program?

Homework Statement


Consider a stepped beam shown in below. The beam is statically indeterminate and a concentrated force P is applied at B. As shown in the figure, the segments of AC and CD have the rigidities of EI1 and EI2, respectively. Determine the deflections at B and C using singularity functions. Note: You might need to use a symbolic equation solver (Matlab, Mathematica, etc.) to solve simultaneous equations.
media%2Fef6%2Fef6053ee-2342-4c31-baf1-f54818f8d65d%2FphpTdrDD3.png

Homework Equations


(below, in my attempt)

The Attempt at a Solution


upload_2018-9-23_16-34-5.png

(I use symbol A in Matlab for F(A) in my handwritten)
upload_2018-9-23_16-39-38.png

Where F(A) should not be in terms of F(A) itself. A, B, D, M suppose all can be expressed in constants (i.e. P L E I1 I2).

By what command can I solve the deflection function (y1 and y2) only in terms of constants (i.e. P L E I1 I2)? Or if my calculation is incorrect? Thank you.
 

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  • #2
You can use Matlab's symbolic equation solver to solve your simultaneous equations. You can use the command "solve" to solve a system of equations, where each equation is written as an expression in terms of the variables you want to solve for.For example, if you have two equations of the form:A = 2*x + 3*yB = 5*x + 7*yThen you can solve for x and y by using the following command:[x, y] = solve(A - 2*x - 3*y, B - 5*x - 7*y)This will give you the solutions for x and y in terms of the constants A and B. You can then plug these solutions into your deflection functions to get the deflection at B and C.
 

1. What is (Matlab) beam deflection solution using symbolic simultaneous equations?

(Matlab) beam deflection solution using symbolic simultaneous equations is a method for determining the deflection of a beam under loading conditions by solving a system of equations symbolically. This allows for a more precise and efficient solution compared to traditional numerical methods.

2. How does (Matlab) beam deflection solution using symbolic simultaneous equations work?

This method works by representing the beam as a series of segments and using the principles of equilibrium to create a system of equations. These equations are then solved symbolically using Matlab, taking into account the beam's geometry, material properties, and loading conditions.

3. What are the advantages of using (Matlab) beam deflection solution using symbolic simultaneous equations?

Some advantages include increased accuracy and efficiency compared to numerical methods, as well as the ability to easily make changes to the beam's properties and loading conditions without having to re-solve the system of equations.

4. Are there any limitations to (Matlab) beam deflection solution using symbolic simultaneous equations?

One limitation is that it may not be suitable for complex beam geometries or loading conditions. Additionally, it requires a good understanding of Matlab and the principles of equilibrium.

5. How is (Matlab) beam deflection solution using symbolic simultaneous equations different from traditional methods?

Traditional methods use numerical techniques, such as finite element analysis, to approximate the beam's deflection. This can be time-consuming and less accurate compared to using symbolic simultaneous equations, which provides an exact solution.

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