Need help finding the restraining reaction force for a beam

In summary: Right, except XA=-XB. And if not zero then it changes YA and YB so as to balance the torque.In summary, the illustrated structure is affected by a known couple, and try to figure out the restraining reaction force of the hinge A and hinge E.
  • #1
Kile
12
0
1. The illustrated structure is affected by a known couple, and try to figure out the restraining reaction force of the hinge A and hinge E.
LW9hyYP.jpg


We should analyse ECD instead. Since arm CD is a two force members, so N(C) in in the direction where CD connects by these two points. The distance from E to diagonal CD is a/√2. So we have N(C)=√2 m/a. Because N(C)=N(E) ( N(C) and N(E) together form a couple), N(E)=√2 m/a.
Where did I go wrong?
 

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  • #2
Kile said:
Where did I go wrong?
I agree with your reasoning and answer. Who says it is wrong? What other answer is given ?
 
  • #3
haruspex said:
I agree with your reasoning and answer. Who says it is wrong? What other answer is given ?
The official answer just doesn't match mine.
 
  • #4
Kile said:
The official answer just doesn't match mine.
Ok, but what is the official answer?
 
  • #5
R_A= \frac m 2a, R_E=\frac \sqrt {{2} m} a,
 
  • #6
Your latex had some errors. In fixing it up I arrived at
Kile said:
##R_A= \frac m{ 2a}##, ## R_E=\frac {\sqrt {2} m} a##,
But that makes the reaction at E the same as you got, so perhaps you meant something else.
 
  • #7
haruspex said:
Your latex had some errors. In fixing it up I arrived at

But that makes the reaction at E the same as you got, so perhaps you meant something else.
Yes. You did it in the right format. Do u know how to get this official answer?
 
  • #8
Kile said:
Yes. You did it in the right format. Do u know how to get this official answer?
As I wrote, it's the same as your answer, just written differently. They both say ##(\sqrt 2)(\frac ma)##.
 
  • #9
How did u get ##N_A## ?
Can u draw a diagram to illustrate?
 
  • #10
Kile said:
How did u get ##N_A## ?
Can u draw a diagram to illustrate?
I thought we were discussing NE.
For NA, take moments about the other hinge.
 
  • #11
How can u get it? can u help me out?
 
  • #12
Kile said:
How can u get it? can u help me out?
Consider the whole frame as one body. If you take the B hinge as axis, what moments are there?
 
  • #13
zcrgSYO.png
Because point B has a pulley on the ground, ##N_B## is vertical.
Choose A be centroid
$$\sum m_A (F)=0, ~2a N_B + m=0$$
$$\Rightarrow N_B=\frac {-m} {2a},$$ So it's downward.
X-axis, $$X_A=0$$
Y-axis, $$Y_A=0 $$ $$N_B + Y_A=0$$
$$\Rightarrow Y_A= -N_B = \frac {m} {2a}$$ So ##Y_A## it's upward.
 

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  • #14
Kile said:
View attachment 240415 Because point B has a pulley on the ground, ##N_B## is vertical.
Choose A be centroid
$$\sum m_A (F)=0, 2a N_B + m=0$$
$$\Rightarrow N_B=\frac {-m} {2a},$$ So it's downward.
X-axis, $$X_A=0$$
Y-axis, $$Y_A=0 $$ $$N_B + Y_A=0$$
$$\Rightarrow Y_A= -N_B = \frac {m} {2a}$$ So ##Y_A## it's upward.
Right... except, strictly speaking there could be equal and opposite horizontal forces at A and B, making the problem indeterminate.
 
  • #15
haruspex said:
Right... except, strictly speaking there could be equal and opposite horizontal forces at A and B, making the problem indeterminate.
You mean $$X_A = X_ B$$ It may not equals to 0.
We just can't calculate it from the information already given.
Is that what you are trying to say here?
 
  • #16
Kile said:
You mean $$X_A = X_ B$$ It may not equals to 0.
We just can't calculate it from the information already given.
Is that what you are trying to say here?
Right, except XA=-XB. And if not zero then it changes YA and YB so as to balance the torque.
 

What is a restraining reaction force for a beam?

A restraining reaction force for a beam is a force that is applied to the beam in the opposite direction of the applied load. It helps to keep the beam stable and prevent it from buckling or collapsing under the load.

Why is it important to find the restraining reaction force for a beam?

Knowing the restraining reaction force for a beam is important for ensuring the structural integrity and safety of the beam. It helps to determine the appropriate support and bracing needed to prevent the beam from failing under the applied load.

How can I calculate the restraining reaction force for a beam?

The restraining reaction force for a beam can be calculated using the equations of static equilibrium. This involves analyzing the forces and moments acting on the beam and setting them equal to zero to solve for the unknown forces, including the restraining reaction force.

What factors can affect the restraining reaction force for a beam?

The restraining reaction force for a beam can be affected by several factors, such as the magnitude and direction of the applied load, the type of support at each end of the beam, and the length and material properties of the beam.

Are there any tools or resources available to help me find the restraining reaction force for a beam?

Yes, there are many online calculators and software programs that can assist in calculating the restraining reaction force for a beam. Additionally, consulting with a structural engineer or referring to engineering textbooks can also provide guidance in determining this force.

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