Pratt Truss Analysis: Get Help From Experts

[boxhunter91]

Pratt Truss Analysis :(

Homework Statement

Hello, first post here.
Been given an engineering assignment for school but not quite understanding how to answer all these questions.

Homework Equations

Was told to use Method of Joints for the reactions on left and right.
And Method of Sections on the forces in the members.

The Attempt at a Solution

Not sure how :(

Please help guys.
Thanks in advance.
boxhunter.

 

[boxhunter91]

Sorry for double post But I really need help for this.
Anyone have any assistance?

 

[mathmate]

Q1.
Consider the truss as a rigid body, the external forces acting on the truss are determinate, so by simply taking moments about each of the two supports, you should have no difficulty finding the reactions.
Q2.
Once the reaction at A is know, there are only three forces at A.
Resolve forces in the X- (horizontal) and Y- (vertical) directions. This will end up with two equations and two unknowns to find forces AB and AC. As it is customary, the bottom chord (AC) is in tension and the top chord is in compression.
BC has zero force, deduced by resolving forces in the Y-direction at joint AC. Therefore force CD equals AC.
Now consider joint B. Since force AB is known, and unknowns are BE and BD for which you can solve again by resolving forces in the X- and Y-directions.
Proceeding this way, joint by joint, you will be able to find all the unknowns requested.
Q3.
Since FD is part of the lower chord, it is in tension. Once you have calculated the force, the strength of the steel and the safety factor, it would be relatively easy to calculate the area required, since a tension member will not be subjected to buckling failure.

 

[boxhunter91]

Thanks mathmate.
For question 1 i got 45kN for the Left support and 40kN for the right.
But now I am not too sure what to do for the 2nd question
Anyone got any ideas?

 

[mathmate]

Very good. You have the correct answer for the reactions.

For question 2, you concentrate on joint A.
Identify the three forces that cross joint A. Compile the magnitude and direction of each. There should be one known force, and two unknowns (Fab and Fac). By resolving the three forces in the x and y directions, you should be able to find Fab and Fac. If you do not know the direction of the forces, assuming any direction (towards or away from A) and note it with an arrow. If the force comes out negative, you simply reverse the arrow.
Work that out for joint A, and if you succeed, you can proceed to other joints. If not, post what you have compiled, and tell me where you got stuck.

 

[boxhunter91]

Here is my attempt at joint A to find AB and AC.
I used trigonometry which is allowed by our school.
im probably wrong but :(
Thanks for your help mathmate.

 

[mathmate]

Your calculations are correct!
Proceed the same way for other joints and you'll crack them all!
Note: Perhaps I don't read well, but AC is 34.75 and I seem to read 39.75.
The direction of forces are correct as well (compression in AB and tension in AC)

 

[boxhunter91]

Wow 2/5 done preety happy. I am just not sure what I am supposed to do when the 10kN downward forces are put onto the joints? Say on Joint E a 10kN force is applied how would I go about finding GE or EF?
Would they be the same?
Like you said earlier CD=AC so how could I find member FD?
Thanks a lot mathmate :D

EDIT: Yeh my 4's look like 9's.

 

[mathmate]

Like you said earlier CD=AC

I deduced that because at joint C, BC is a vertical member with no other forces having a vertical component, so there is no vertical component, therefore BC does not carry any load, i.e. as if it was not there. So CD=AC.

After having solved joint A, you would note the known forces and directions in the diagram. The next soluble joint would be B, since AB is known, and BC=0 as stated above.
In fact, if you do a cursory calculation, you will find that DB and AB are equal in magnitude, but opposite in direction (tension and compression). This allows you to calculate joint BE.
After you have noted the calculated forces, then you will find that the next soluble joint is D, and so on. The vertical external force does not add unknown forces, just the known ones, so you'd have an extra known force to account for.

Keep going at it, and post any time.

 

[boxhunter91]

The vertical external force does not add unknown forces, just the known ones, so you'd have an extra known force to account for.

Not sure what you mean by that :S.
I've calculated both CD and BD and you were right they were the same except BD was a tensile force. How do I go about proving BE with the 10kN load on the E joint?
Same for the D joint.
Regards.

 

[mathmate]

In a truss analysis, you have to proceed joint by joint, in the order of availability of data.
You have correctly started with the A joint, and if you have written down the forces on the diagram as I suggested, you will see that the only joint that has two or less unknowns is B. Resolve the forces into x and y as in joint A in order to find BE and BD.
You have found BD by a short cut, so if you write down the forces on the diagram, you will see that there are two joints having 2 unknown forces or less (B and D).
Proceed this way joint by joint, and you will have no problem solving them all.

 

[boxhunter91]

Ok this is my working out Members GE, FD, EF
Thanks mathmate.

 

[mathmate]

Good!
You can also take moments of forces on the right side, so there will be less forces to take care of.
When you take moments, take about a joint, and not in the middle of a member.
The calculations for GE is incorrect because it should be 6 and not 6.5 if you take moments about the joint F.