# What mistake did I make in finding the reaction at hinge A?

• gnits
In summary, the conversation involves a person asking a question about finding the reaction at the hinge A and providing their own calculations, which differ from the answer given in the book. The person then realizes that their answer is actually correct and the book's answer contains an error. The error is identified as a decimal place blunder and the direction of the reaction is clarified.
gnits
Homework Statement
To find forces in a framework
Relevant Equations
Equating of forces
Moments
A very simple (I thought!) question:

I'm just looking at the first part, finding the reaction at the hinge A.

Here is my annotated diagram, with the reaction and A resolved into it's X and Y components, the force at E labelled as Fe and the length of ED labelled as L.

Considering the body as a whole:

Resolving vertically:

Ya = 500

Xa * L = 2 * L * 500

which gives Xa = 1000

So the resultant at A will have size sqrt(1000^2 + 500^2) = 1118 (approx.)

Answer given in book is 112 N at 26.6⁰ below the horizontal.

My answer is very different and also above the horizontal.

What simple mistake have I made in my reasoning?

Thanks.

The answer given in the book is not correct, yours is.

Thanks, that's a relief. The book has rarely been wrong and so I was all too ready to doubt myself. Much appreciated.

Lnewqban
gnits said:
Thanks, that's a relief. The book has rarely been wrong and so I was all too ready to doubt myself. Much appreciated.
The book's error in the magnitude is clearly just a decimal place blunder.
Above or below horizontal is inadequate to define the direction. Given the angle it makes to the horizontal, there are four possible directions. Up and to the left can be thought of as above horizontal, viewing it as a motion in that direction from A. But it can be viewed as below horizontal when considering the diagonal line through A that it lies on: first and third quarters = above horizontal, second and fourth quarters = below horizontal.

## 1. What is a framework in the context of finding forces?

A framework is a structure made up of interconnected members or elements that are subject to external forces. It is used to analyze and determine the internal forces acting on each member of the structure.

## 2. How do you determine the forces in a framework?

To determine the forces in a framework, you must first draw a free body diagram of the entire structure, then apply the equations of static equilibrium to each joint or connection point. This will allow you to solve for the unknown forces acting on each member.

## 3. What are the different types of forces that can act on a framework?

The different types of forces that can act on a framework include tension, compression, shear, and bending. Tension forces pull on a member, while compression forces push on a member. Shear forces act parallel to the surface of a member, and bending forces cause a member to bend or deform.

## 4. How do external loads affect the forces in a framework?

External loads, such as weight or applied forces, can cause a framework to experience internal forces. These forces can be calculated using the equations of static equilibrium and taking into account the direction and magnitude of the external loads.

## 5. What are some common methods used to analyze forces in a framework?

Some common methods used to analyze forces in a framework include the method of joints, which analyzes forces at each joint, and the method of sections, which involves cutting a section of the framework and analyzing the forces acting on that section. Other methods include the method of virtual work and the method of consistent deformations.

• Introductory Physics Homework Help
Replies
5
Views
916
• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
960
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
1K