Mechanics of Solids - weight problem

[Moskmeister]

Summary: How much weight can the bars support?

Three one-meter-long bars with cross-section area A = 1 square centimeter support a rigid plate of weight W. For steel, E = 200 GPa and S = 400 MPa. Determine the maximum weight W the bars can support for three cases:
(i) all three bars are exactly 1m long
(ii) the outer bars are exactly 1m long but the middle bar is 0.999m
(iii) the outer bars are exactly 1m long but the middle bar is 1.001m

The configuration: the three bars are upright, side by side like this l l l with the weight being a big block on top of them.

How do I use the elongation = NW/EA to find the weight the bars can support? How does strength factor into that equation? And doesn't S = W/A?

 

[phinds]

Are we supposed to guess the configuration you are talking about?

 

[Moskmeister]

Are we supposed to guess the configuration you are talking about?

Facepalm. Just edited it. Thanks.

 

[jrmichler]

The first problem (all three bars equal length) is straight from the chapter on statically indeterminate systems. Solve that first. Then, and ONLY then, look at the other two problems.

It is very common for students to trap themselves by trying to solve the entire problem in one step. When confronted by a problem where you cannot see a path to the solution, start by solving what you can. Then look at the next part (or next problem) in light of what you learned so far.

This is also the technique for solving the complex, multistep problems that you will encounter on the job.

 

[Moskmeister]

I can’t find any problem like this in that chapter

 

[jrmichler]

That means that this is the course where you start to transition from high school science (memorize the chapter to ace the exam) to college science, where you have to understand the principles to solve the problems. The basic principle of statically indeterminate systems is the number of unknowns is greater than the number of equations.

You have one equation where the sum of forces equals zero, a second equation where the sum of moments equals zero, and three unknowns. The unknowns are the forces in the three bars. Your task is to find a third equation.

Hint #1: That equation uses the stiffness of the three bars.

Hint #2: Assume that you will see many more problems that cannot be solved by finding a similar example problem. Learn how to study the concepts in the chapter and apply them to a problem that does not match an example problem.

Hint #3: Use the example problems to find if you understand the principles.

Hint #4: Sometimes this is not easy.

BTW, my own decision rule as an undergrad was to either give up and move on, or seek help, only after working on a single problem for eight hours.

 

[Chestermiller]

Are the bars touching each other, or are they separated? If so, by how much? What is the exact geometry?

 

[PhanthomJay]

It should be noted that the plate is rigid. Therefore it cannot bend. What does that tell you about the deformation of the bars when the plate is in contact with them?