Solving Pinned Jointed Frame Exterior Reactions

  • Thread starter matthew_hanco
  • Start date
  • Tags
    Frames
In summary, the problem is to find the exterior reactions and how to work them out, taking moments and summing forces. The horizontal and vertical reactions can be calculated using the sum of horizontal and vertical forces. The numbers for the reactions should be roughly HA=20, VA=10, and HE=15, but more accurate calculations are needed. The lecturer's answer for the resultant reaction force at point A is 22.20 kN, but the orientation angles given are incorrect. The correct dimensions of the structure are needed to find the correct angles and resultant forces.
  • #1
matthew_hanco
19
0
The problem is attached to this post, basically i need the exterior reactions and how to work them out.

i know i need to take moments I am just not sure how to work it out.


Basically what i worked out

is

i assumed horizontal members are equally to 1

sum of the horizontal = 0 5Kn- HA - HE=0

Sum of the vertical =0 10KN- VA =0

But that is where I am stuck i know the numbers should be roughly

HA=20
VA= 10
HE = 15

But i know it is more accurate than that I am not sure if i need to include sine or cosine in the solution

Thanx in advance
 

Attachments

  • problem.png
    problem.png
    5 KB · Views: 417
Physics news on Phys.org
  • #2
To add to it i have just tried

sum MA= 0

Therefore he x 2 - 5x1 - 10x2 =0

he =12.5

sum of horizontal 5+12.5 =17.5

therefore ha = -17.5

sum of the vertical

Va -10 x 1 =0

so Va = 10

Is that right?
 
  • #3
Im desperate and really need someones help urgently.
 
  • #4
matthew_hanco said:
sum MA= 0

Therefore he x 2 - 5x1 - 10x2 =0

he =12.5

Hi matthew,
Since you're taking moments around A and since the 5 kn and 10 kn forces produce opposite moments around A, one of your terms needs to be positive and one needs to be negative. You have a negative moment around A for BOTH of these forces.

Once you get the horizontal force from E you can sum forces and get the horizontal and verticle forces on A.
 
  • #5
ok so the new calculated resultant forces would be

He= 15 ( (-10 x 2) - (+5x1) + He=0)

Ha= -20 (+15 + 5 - ha= 0 therefore Ha= -20)

Va= -10 (+10 -Va=0)


But now checking my lecturers answers he gives

14.82 for He

And a resultant force for a 22.2 acting 26.46 degrees from the horizontal


But with my results the resultant for a is 22.36 and 26.56 from the horizontal.

who is right, if he is how can i account for the discrepencies
 
  • #6
Those answers are all pretty close, so I would guess the differences are in rounding error. Regardless, I can't check the math because the figure you provide has no dimensions on it.
 
  • #7
All forces are in KN
 
  • #8
I can see the forces. There are no linear dimensions on your picture.
 
  • #9
matthew_hanco: The dimensions are already fully defined by the diagram given in post 1. The resultant reaction force at point A from your lecturer, 22.20 kN, is correct. However, the orientation angles given by both you and your lecturer are currently incorrect. The resultant reaction force at point A is 22.20 kN acting 26.77 deg from the horizontal. Keep trying. Your discrepancies are not due to round-off error. First, figure out the correct dimensions of your structure, and label them on your free-body diagram. You currently appear to be using wrong dimensions.
 
  • #10
Got it, the length should be root 3 instead of 1.

so it should be

(-10 x (root3x2) - +5x1)/2=Ha
 
  • #11
Excellent, matthew_hanco.
 

1. What is a pinned jointed frame?

A pinned jointed frame is a structural system made up of interconnected members joined together at their ends with pinned connections. These connections allow for rotation or movement at the joint, creating a flexible structure.

2. How do you solve for exterior reactions in a pinned jointed frame?

To solve for exterior reactions in a pinned jointed frame, you need to use the principles of static equilibrium. This means that the sum of all forces in the horizontal and vertical directions must equal zero, and the sum of all moments at any point must also equal zero. By setting up and solving these equations, you can determine the reactions at the exterior joints of the frame.

3. What information do you need to solve for exterior reactions in a pinned jointed frame?

To solve for exterior reactions in a pinned jointed frame, you will need to know the loads acting on the frame, the locations of those loads, and the geometry of the frame (lengths of the members and angles between them). You may also need to know the properties of the materials used in the frame, such as their strength and stiffness.

4. Can you solve for exterior reactions in a pinned jointed frame using software or do you need to do it by hand?

Yes, it is possible to solve for exterior reactions in a pinned jointed frame using software. Many structural analysis programs have the capability to solve for reactions in a variety of structural systems, including pinned jointed frames. However, it is important to have a basic understanding of the principles and equations involved in order to use the software effectively.

5. Are there any common mistakes to watch out for when solving for exterior reactions in a pinned jointed frame?

One common mistake when solving for exterior reactions in a pinned jointed frame is forgetting to account for all the forces and moments acting on the frame. It is important to carefully consider all the loads and their locations, as well as any additional forces or moments caused by the flexibility of the connections. Another mistake is using incorrect units or not converting units properly, which can lead to incorrect solutions.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
20
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
785
  • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Back
Top