# Mechanics of Solids - weight problem

• Moskmeister
In summary, the bars can support a weight of up to W if they are all exactly 1m long, if the middle bar is 0.999m long, or if the middle bar is 1.001m long.
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?

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

phinds said:
Are we supposed to guess the configuration you are talking about?
Facepalm. Just edited it. Thanks.

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.

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

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.

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

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?

## 1. What is the weight of an object?

The weight of an object is the force exerted on it by gravity. It is measured in units of mass, such as kilograms or pounds, multiplied by the acceleration due to gravity (9.8 m/s^2).

## 2. How does the weight of an object change on different planets?

The weight of an object on different planets will vary due to differences in gravitational pull. The greater the mass of the planet, the greater the gravitational pull and therefore the greater the weight of an object. For example, a person who weighs 150 pounds on Earth would weigh approximately 57 pounds on Mars and 354 pounds on Jupiter.

## 3. What is the difference between weight and mass?

Weight and mass are often used interchangeably, but they are actually two different measurements. Mass is a measure of the amount of matter in an object, while weight is a measure of the force exerted on an object by gravity. Mass is constant, while weight can vary depending on the strength of the gravitational pull.

## 4. How is weight calculated?

Weight is calculated by multiplying an object's mass by the acceleration due to gravity. The formula for weight is W = mg, where W is the weight in newtons, m is the mass in kilograms, and g is the acceleration due to gravity (9.8 m/s^2 on Earth).

## 5. How does the weight of an object affect its stability?

The weight of an object can affect its stability by influencing its center of gravity. The center of gravity is the point at which an object's weight is evenly distributed. If an object's weight is not evenly distributed, it can become unstable and topple over. Objects with a lower center of gravity are generally more stable than those with a higher center of gravity.

• Introductory Physics Homework Help
Replies
20
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
4K
• Engineering and Comp Sci Homework Help
Replies
4
Views
16K
• Classical Physics
Replies
86
Views
4K
• Mechanical Engineering
Replies
8
Views
3K
• Introductory Physics Homework Help
Replies
22
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
4K
• Mechanical Engineering
Replies
2
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K