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howslifebrah

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- 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 MCB 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!

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 MCB 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!