Mechanics Test: Calculating Forces in a Mechanical Framework

[optrix]

Hi all, I'm doing some last minute revision for a mechanics test, and I'm going through a practice paper. I'm stuck on one question about mechanical frameworks. Here is a picture of the framework:

(It seems I can't display the image directly in my post on this forum)

The problem is to calculate the force, and identify the type of force (tensile or compressive) in each member of the framework. Heres what I've done so far:

Calculated the reaction forces:

Resolving vertically:

4kN+3kN+5kN=R$$_{R}$$+R$$_{R}$$
R$$_{R}$$+R$$_{R}$$=12kN

taking moments about L (where R_L is acting):

-4k*2-3k*4-5k*6+R$$_{R}$$*8 = 0
R$$_{R}$$*8 = 50kNm
R$$_{R}$$ = 50k/8 = 6.25kN

R$$_{L}$$= 12k - R$$_{R}$$ = 12k - 6.25k = 5.75k

From this point I'm not sure how to proceed and find the value and type, of the force in each meber of the framework. (9 members)

From the two angles given (30') I can calculate all the rest of the angles in the framework, but I'm not sure it thata helps anything.

Really appreciate some help, thanks alot.

 

[optrix]

Here is the image:

http://img118.imageshack.us/img118/8145/dsc00157ws1.jpg [Broken]

 

[Fantastic Fox]

Your answers for the first part are right.


To calculate the force, and identify the type of force (tensile or compressive) in each member of the framework:

Look at each joint separately. Draw a FBD of the joint showing all the forces acting on it. Use basic trig and the equations ΣF(x direction) = 0 , ΣF(y direction) = 0 to calculate the forces.
For the unknown forces in each member, you can assume they are either tensile or compressive. I usually assume all the unknown forces are tensile, and if it turns out that they are compressive you'll get a negative value. When drawing the FBD, tensile forces act away from the joint, compressive forces act towards the joint.
When you have all joints examined except the last one, you'll find you've worked out the forces in each member, but examine the last joint to check your results.

I did the first joint (I chose the joint on the left where R_L acts). If you want to check your result I'll tell you what I got, or I could scan it up if you want to see.

It's simply a case of working your way through all the joints doing the same thing 8/9 times.

Hope that helps,
Fantastic Mr. Fox

 

[optrix]

Thanks a lot for the fantastic reply, fox! I managed to find a page about 'the joint method', and was slowly picking it up before I read this. I was still unsure about how to find out whether the forces are compressive or tensile, but have been calculating a few values, so thanks.

Anyway, This is the labelled diagram I re-drew myself:

http://img138.imageshack.us/img138/1143/dsc00159yi7.jpg [Broken]

And this is the FBD of joint A in the lower left corner, along with my calculations:

http://img185.imageshack.us/img185/8333/dsc00160mx0.jpg [Broken]

So I got F[AF] = 3.32kN, and F[AB]=11.5kN I still wasn't able to work out whether they were compression or tension though. So tensile forces will act away from the joint, and compressive forces towards it? I just drew the FBD (second link) how I expected the forces to be orientated, but when my answers came out, they were both positive.

 

[Fantastic Fox]

Your value of F[AB] is correct. They way you have drawn it actually shows it as being compressive (acting towards the joint), so a positive value is correct in that situation.

Your value of F[AF] is incorrect. tan30 = 5.75 / F[AF] => F[AF] = 9.96kN (tensile) Check your geometry.

There's a nicer way to draw the FBD, which is much clearer in my opinion. I'm too tired to post it now. But briefly, from your FBD (triangle), where the 5.75kN meets the F[AF], draw a little dot representing the joint. Draw the F[AB] at an angle +30degrees to F[AF] (just like the framework looks in your previous diagram {the three forces intersect at that single point}) with the arrow pointing away assuming tensile, or towards assuming compressive. Calculate the forces using ΣF(x direction) = 0 , ΣF(y direction) = 0. I'll try to describe that better or post an image in the next 24 hours.

 

[optrix]

Thanks alot, I understand my mistake, I made the error of tan() = adjacent / opposite, when it should be tan()= opposite /adjacent.

I'll try what you suggested tonight before I go to bed (I'm very tired too :) ), and I'll get back tommorrow. Thanks for all the help.

 

[optrix]

Hi, I tried your method of just drawing the forces on the pin, rather than trying to form a triangle of forces, and I find it much easier...it's also better for determining tensile or compressive.

Here's my working for the first joint (A):

http://img261.imageshack.us/img261/188/dsc00162qn8.jpg [Broken]

I hope you can read it. If not, I assumed the forces were tensile (away from joint) and I got -11.5kN for F[AB], showing it is in compression, and 99.6kN for F[AF] showing it's in tension.

I've done it on the rest now too, and think I've got it sorted (Though we weren't given answers with the practice test ). Thanks

 

[Fantastic Fox]

I would suggest that you keep all forces in kN, as there isn't a need to convert to N. I think that led you to a little error. Check your calculation of 99.6kN, you're out by a factor of ten.

Looks like you're on the right track anyway. When you examine the last joint, you'll have already calculated all the forces, but use the equations ΣF(x direction) = 0 , ΣF(y direction) = 0 to check your results. If the last joint works out, you're usually correct.

 

[optrix]

Oh yeh, it should be 9.96kN. I'm feeling pretty confident about these questions now, so thanks for the help.