# Equilibrium of a T-Shaped Bracket: Determining Reactions at A and C

• tacet777
In summary, Homework Equations state that:\-\SigmaFx=-Ax+Cx+Bx-Asin(\alpha)+Cx+Bsin(\alpha)=0-\SigmaFy=Ay+Cy-By-Acos(\alpha)+Cy-Bcos(\alpha)=0-Mc=-(30)Asin(\alpha)-(15)Acos(\alpha)+(30)Bsin(\alpha)+(25)Bcos(\alpha)
tacet777

## Homework Statement

A T-shaped bracket supports a 150-N load as shown. Determine the reactions at A and C when (a) $$\alpha$$=90o, (b) $$\alpha$$=45o

ans: (a)A=150N going down, C=167.7N,63.4degrees (b)A= 194.5N going down; C=253N, 77.9degrees
base on the book.

http://www.glowfoto.com/static_image/23-165339L/2124/jpg/07/2010/img6/glowfoto
[URL]http://www.glowfoto.com/static_image/23-165339L/2124/jpg/07/2010/img6/glowfoto[/URL]

## Homework Equations

$$\Sigma$$Fx=0 ;right +
$$\Sigma$$Fy=0 ;up +
$$\Sigma$$M=0 ;clockwise +

## The Attempt at a Solution

$$\Sigma$$Fx=-Ax+Cx+Bx
-Asin($$\alpha$$)+Cx+Bsin($$\alpha$$)=0
$$\Sigma$$Fy=Ay+Cy-By
Acos($$\alpha$$)+Cy-Bcos($$\alpha$$)=0
Mc=-(30)Asin($$\alpha$$)-(15)Acos($$\alpha$$)+(30)Bsin($$\alpha$$)+(25)Bcos($$\alpha$$)

substituting the $$\alpha$$=90degrees

A=150N (but i don't know how to check weather it is going down or up since i got it in the moment equation)

using A=150
Cx=0
Cy=0Thank you guyz...

Last edited by a moderator:
tacet777 said:

## Homework Statement

A T-shaped bracket supports a 150-N load as shown. Determine the reactions at A and C when (a) $$\alpha$$=90o, (b) $$\alpha$$=45o

ans: (a)A=150N going down, C=167.7N,63.4degrees (b)A= 194.5N going down; C=253N, 77.9degrees
base on the book.

## The Attempt at a Solution

$$\Sigma$$Fx=-Ax+Cx+Bx
-Asin($$\alpha$$)+Cx+Bsin($$\alpha$$)=0
$$\Sigma$$Fy=Ay+Cy-By
Acos($$\alpha$$)+Cy-Bcos($$\alpha$$)=0
Mc=-(30)Asin($$\alpha$$)-(15)Acos($$\alpha$$)+(30)Bsin($$\alpha$$)+(25)Bcos($$\alpha$$)

substituting the $$\alpha$$=90degrees

A=150N (but i don't know how to check weather it is going down or up since i got it in the moment equation)

using A=150
Cx=0
Cy=0

Does force A have a horizontal component? Can we not assume that Ax=0 since it is supported by a roller?

Even if force A had both horizontal and vertical components, do not use the same variable name for both A and B (don't use $$\alpha$$ twice).

Once you assume the direction of your forces, you must keep to that assumption in all of your equations. Some problems will be obvious, others will not. If your answers are negative, you assumed the wrong direction (it doesn't matter if your initial assumption is correct). Just be sure to state the vector directon correctly in your final answer.

When you create your moment equation, the directions of the forces that cause the moments must be the same as those in your force equations.

Assuming the Ay pushs down (wouldn't work very well otherwise), Cx pushes to the left (only horizontal force available to oppose force B) and Cy pushes up, your first equations should be:

Ax=0 (assume due to roller)
$$\Sigma$$Fx = 0
Bsin($$\alpha$$) - Cx = 0

Try to create the others again yourself.

The answers you list above (from your book?) appear to incorrect (by my calcs). The directions are correct, but the magnititudes are wrong.

A good way to determine force directions in this case is: (1) recognise that there are just 3 forces acting on the bracket (2) for equilibrium these forces must all meet at one point. You should be able to identify that point (3) draw the triangle of forces, knowing the magnitude of just one, but the directions of the others.(4) put arrows on the sides of the triangle for all the known forces i.e. 150 N (5) put on the other arrows, making sure the arrows go round the triangle cyclically. That is, all cw or acw. These arrows are then in the correct directions for the unknown forces. The magnitudes of the forces should also agree with the trig/algebraic approach, thus making your request for confirmation unnecessary.

## What is a T-shaped bracket support?

A T-shaped bracket support is a type of bracket that is shaped like the letter "T". It is commonly used in construction and engineering to provide support and stability for various structures and objects.

## What materials are T-shaped bracket supports typically made of?

T-shaped bracket supports can be made from a variety of materials, including metal, wood, and plastic. The choice of material depends on the specific application and the amount of support needed.

## How do T-shaped bracket supports work?

T-shaped bracket supports work by distributing the weight of an object or structure evenly across its arms. This helps to prevent the object from shifting or collapsing under its own weight.

## What are some common uses for T-shaped bracket supports?

T-shaped bracket supports are commonly used in construction for supporting beams and joists, as well as in furniture for stabilizing shelves and other components. They can also be used in DIY projects for creating custom shelving or storage solutions.

## Are there any alternatives to using T-shaped bracket supports?

Yes, there are several alternatives to using T-shaped bracket supports, including L-shaped brackets, corner braces, and angle brackets. The choice of bracket will depend on the specific application and the desired level of support.