# Beam and Hinge Equilibrium Analysis

• sinequanon
In summary, the tension on the cable, the force on the hinge, and the angle of the reactant force are
sinequanon
1. Homework Statement

A 10 meter beam with a mass of 100 kg is hinged at the wall with a supporting cable at 6 meters from the hinge, making a 60 degree with the beam. There is a 50 kg person located at 9 meters from the hinge. Assuming equilibrium, what is the tension on the cable, the force on the hinge, and the angle of the reactant force.

2. Homework Equations

1. ΣFx = Rx - TcosΘ = 0

2. ΣFy = Ry + TsinΘ - Fobject - Fbeam = 0

3. TsinΘ(dcable) - Fbeam(dbeam) - Fobject(dobject)

*Use 10 m/s2 for the value of gravitational acceleration.

3. The Attempt at a Solution

Alright, so I just wanted to double check to see if I'm actually doing this correctly.

First I substitute into the third equation in order to find the cable tension.

Tsin60(10 m) - (1000 N)(5 m) - (500 N)(9 m) = 0
T = -3116.68 N

My first question is with that bolded segment: is it correct to have it subtracted if I'm looking for T? Should it be added instead since the direction is clockwise?

If that's right, then I need to find the force on the hinge, and here is where I really find trouble.

ΣFx = Rx - 3116.68cos60 = 0
Rx = 2968.36 N

Okay, that part was easy for me, but...

ΣFy = Ry + 3116.68sin60 - 1000 - 500 = 0
Ry = 1199.12

I asked my instructor about this, but he insists this is incorrect (which I'm sure it is). He is telling me to use

6F +1000(1) = 500(3)

I have only a vague understanding of what is involved in this equation. Could someone help me wrap my head around this a little better?

Tsin60(10 m) - (1000 N)(5 m) - (500 N)(9 m) = 0

The cable is attached at 6m from the hinges. So check the equation again.

6F +1000(1) = 500(3)

With this equation you can find the force on hinges. Here the moments of couple are taken about the point of suspension of the cable to the beam.

Last edited:
Ah. Well, that was pretty careless of me. Thanks for that.

Okay, so...

Tsin60(6 m) - (1000 N)(5 m) - (500 N)(9 m) = 0
T=1828.28

I take it I would be correct with using subtraction in that equation then?

Rx - 1828.28cos60=0
Rx=914.14 N

However, I still would like confirmation on which equation to use if finding the force acting on the hinge.Sorry, just saw your edit.

Ah. That explains it so much better. So that will solve for the force on the hinges but will I still need to find Ry in order to find the angle of the reactant force?

Find F. Using F and Rx you can find angle of reactant force.

## 1. What is the difference between a beam and a hinge?

A beam is a structural element that is designed to resist bending and carry loads. It is typically a long, straight piece of material, such as wood or steel. A hinge, on the other hand, is a type of joint that allows two pieces of material to rotate or pivot relative to each other.

## 2. What are some common examples of beams and hinges?

Some common examples of beams include bridges, floor joists, and roof trusses. Hinges can be found in doors, cabinets, and other types of furniture.

## 3. How can I tell the difference between a beam and a hinge?

Beams are typically longer and thicker than hinges. They also usually have a uniform cross-section, whereas hinges have a distinct joint or pivot point. Additionally, beams are designed to resist bending, while hinges are designed to allow rotation.

## 4. Can beams and hinges be used together in a structure?

Yes, beams and hinges can be used together in a structure. In fact, many structures, such as bridges and doors, rely on a combination of beams and hinges to function properly. However, it is important to ensure that the design and installation of these elements is done correctly to avoid any confusion or structural issues.

## 5. How can I prevent confusion between beams and hinges in my project?

To prevent confusion between beams and hinges in your project, it is important to clearly understand the function and purpose of each element. This can be achieved by consulting with a structural engineer or referring to building codes and standards. It is also important to carefully label and differentiate between beams and hinges in your project drawings and plans.

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