# Struggling with a Structural Analysis Problem?

• Engineering
• howslifebrah
In summary, the conversation discusses a problem in the Mechanics of Materials section which involves Structural Analysis. The person is teaching themselves through Youtube lectures, but they feel they may be lacking some critical information. They have attempted to solve the problem using different methods such as simplifying the frame and using force and moment equilibrium equations, but have not been successful. They then verified the answer using frame calculators and found that using the force method is too cumbersome and not what the problem statement is asking for. They suggest using the slope deflection method and assume it is a sway frame with vertical displacement at joint C, but run into a contradiction between their slope deflection equations and the moment equilibrium equation at joint C. They have exhausted their ideas and are seeking guidance
howslifebrah
Homework Statement
Hello everyone,

I am currently studying for an Mech Eng. Master's Program Entrance exam and am reviewing past test problems from the University website.

Problem statement:

Answer the following four questions (45 min limit):

(1) Draw the deformed schematic shape of the bar A-C-B on your answer sheet. (3 points)
(2) Obtain the shearing force and bending moment at Point C. (4 points)
(3) Virtually cut the bar at Point C and assume two cantilevers: AC and BC. Obtain P1, P2, M1, and M2. P1 and P2 are sharing forces at Point C for cantilever AC and BC, respectively. M1 and M2 are bending moments at Point C for cantilever AC and BC, respectively. (12 points)
(4) Obtain the vertical displacement at Point C, δCV. (6 points)

I am currently stuck on part 3.
Relevant Equations
I am not allowed any reference material during the exam. This question seems very similar to the process of Slope-Deflection method for indeterminate frames so I believe it may be related.
Diagram of the problem below. I have 45 minutes to finish all parts of this question without reference material.

The Mechanics of Materials section of these tests are largely Structural Analysis, which I was not taught to this level in my undergrad degree so I am teaching myself via Youtube lectures. I think I must be lacking some critical information to solve some of the problems and I have no guidance so I am hoping for a push in the right direction here.

My first attempt at this problem has involved simplifying the I frame into a double fixed-end beam of length 4L with a CCW moment of 4PL and a downwards point load of 2P centered at 2L (shown below). However making virtual cantilevers from this point and using force and moment equilibrium equations has only been confusing when I tried to work it out. My attempt is not even remotely obeying equilibrium so please ignore it.

I then verified what the answer should be using the results of 2 frame calculators.

I was able to arrive at the same result as the calculator by using force method but that method is *considerably* too cumbersome to use given the test time and not what is being asked by the problem statement.

My gut feeling for a next step is that this can be solved by using slope deflection method. I assumed this is a sway frame with vertical displacement occurring at joint C. However, when I apply that method I run into a contradiction between my slope deflection equations for CA and CB and my moment equilibrium equation at joint C.

Equilibrium equations derived below:

MCB-MCA-MCD=0

However since there is no external loading on members AC and BC, my slope deflection equations for M
CB and MCA perfectly cancel each other while MCD= 4PL. At this point I've exhausted my ideas. I'm hoping someone here can get me on track. Thanks!

DeBangis21

It sounds like you are on the right track by considering the slope deflection method. However, it is important to note that this method can only be used for statically determinate structures. If the structure is statically indeterminate, then you will need to use other methods such as the moment distribution method or the stiffness method.

In order to determine if the structure is statically determinate or indeterminate, you can use the equation: 3n = 2j + r, where n is the number of members, j is the number of joints, and r is the number of support reactions. If this equation is satisfied, then the structure is statically determinate and can be solved using the slope deflection method.

If the structure is statically indeterminate, then you will need to use other methods such as the moment distribution method or the stiffness method. These methods can be more cumbersome, but they are necessary for solving indeterminate structures.

It is also important to make sure that your assumptions and simplifications are correct before attempting to solve the problem. Double check your diagram and make sure it accurately represents the given information. If you are still struggling, it may be helpful to seek guidance from a professor or tutor who is knowledgeable in structural analysis. Keep practicing and don't give up, you will get the hang of it eventually. Good luck!

DeBangis21

## 1. How do I approach a structural analysis problem?

The first step in approaching a structural analysis problem is to carefully read and understand the problem statement. Then, identify the given information and any relevant equations or principles that can be applied. Next, draw a clear and accurate diagram of the structure and label all known and unknown variables. Finally, use the appropriate equations and principles to solve for the unknown variables.

## 2. What are the common challenges in solving a structural analysis problem?

Some common challenges in solving a structural analysis problem include identifying the correct equations and principles to use, determining the appropriate boundary conditions, and dealing with complex geometry or loading conditions. It is also important to check for any mistakes or errors in calculations and to ensure that the final solution makes physical sense.

## 3. How do I check the accuracy of my structural analysis solution?

To check the accuracy of your structural analysis solution, you can compare it to a known or expected solution, if available. You can also perform a sensitivity analysis by varying the input parameters and observing the effect on the output. Additionally, checking for units consistency and using basic engineering principles can help verify the accuracy of your solution.

## 4. What are some useful tools for solving structural analysis problems?

There are various software programs and online calculators available for solving structural analysis problems. These tools can help with complex calculations, visualization of the structure, and automating the solution process. However, it is important to have a good understanding of the underlying principles and assumptions used in these tools.

## 5. How can I improve my skills in solving structural analysis problems?

Practice is key to improving your skills in solving structural analysis problems. It is also important to have a strong foundation in mathematics and engineering principles. Additionally, seeking guidance from experienced engineers and learning from their problem-solving approaches can also be helpful. Continuously challenging yourself with more complex problems can also help improve your skills.

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