Mechanics of Materials: Simple moment question?

In summary, the conversation discusses the analysis of a long retaining wall braced by wood shores supported by concrete thrust blocks. The wall and shores are idealized and the pressure of the soil is assumed to be triangularly distributed, resulting in a force of 190 kN on a 3m length of the wall. The question asks for the compressive stress on part C of the shores, with a given cross-section. The conversation also mentions the use of moments and equilibrium equations in solving the problem.
  • #1
Seraph042
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0

Homework Statement


A long retaining wall is braced by wood shores set at an angle of 30 degrees and supported by concrete thrust blocks. The shores are evenly spaced, 3m apart.

For analysis purposes, the wall and shored are idealized. Note that the base of the wall and both ends of the shored are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force action on a 3m length of the wall is 190 kN.

If each shore has a 150mm x 150mm square cross-section, what is the compressive stress on part C in the shores?



Homework Equations


This is in part 1.2 of my book, labeled 'Normal Stress and Strain', and they give equations of moments as:
Mx = P[tex]\overline{y}[/tex]
My = -P[tex]\overline{x}[/tex]

http://img101.imageshack.us/img101/9463/128mn6.th.png

The Attempt at a Solution



I honestly have no idea where to begin, the book has been no help with these problems, as there is almost no information or examples on how to solve this type of problem.

Please help!
 
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  • #2
Seraph042: You know the direction of the force in member BC, right? Can you break that force into horizontal and vertical components?

Secondly, have you heard of equilibrium, and the three equilibrium equations in statics? Draw a free-body diagram of member AB, and use the equilibrium equations to solve for the reaction forces at points A and B.
 
  • #3


Hello,

Thank you for your question about the mechanics of materials. It seems like you are struggling with a simple moment question involving a long retaining wall and wooden shores. Without seeing the specific diagrams or equations from your book, it is difficult for me to give you a complete answer. However, I can provide some general guidance and steps to help you solve this problem.

1. First, make sure you understand the given information and assumptions. It is important to understand the idealization of the wall and shores, as well as the assumptions about the soil pressure and resultant force.

2. Next, draw a free-body diagram of the 3m length of the wall. This will help you visualize the forces acting on the wall and determine the direction and magnitude of the forces.

3. Use the equations of moments given in your book to calculate the moment at point C. Remember to use the perpendicular distance from the point of rotation (in this case, the base of the wall) to the line of action of the force.

4. Once you have the moment at point C, you can use the equation for bending stress (sigma = My/I) to calculate the compressive stress on part C of the shores. Make sure to use the appropriate moment of inertia for the cross-section of the shores.

5. Finally, don't forget to convert the units to the correct format (e.g. kN to N) and check your answer for reasonableness.

I hope this helps you get started on solving your problem. Remember to always double check your calculations and assumptions, and don't hesitate to ask for clarification if needed. Good luck!
 

Related to Mechanics of Materials: Simple moment question?

1. What is the definition of a moment in mechanics of materials?

A moment is a measure of the force applied to an object in a rotational manner. It is calculated by multiplying the magnitude of the force by the distance from the point of rotation to the line of action of the force.

2. How is a simple moment calculated?

A simple moment is calculated by multiplying the force applied to an object by the perpendicular distance from the point of rotation to the line of action of the force. This distance is known as the moment arm or lever arm.

3. What is the difference between a positive and negative moment?

A positive moment indicates that the rotation caused by the force is in a counterclockwise direction, while a negative moment indicates a clockwise rotation. This is based on the right-hand rule, where the fingers of the right hand curl in the direction of rotation.

4. How does the magnitude of a moment affect an object?

The greater the magnitude of a moment, the greater the rotational force applied to an object. This can cause the object to rotate or deform, depending on the strength and stiffness of the material.

5. What are some common applications of simple moments in mechanics of materials?

Simple moments are commonly used in structural engineering to analyze the stability and strength of buildings and bridges. They are also used in designing mechanical components such as beams and columns to ensure they can withstand the forces and moments applied to them.

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