ASSIGNMENT 6 TRUSS TO SOLVE #1
The truss problem for this semester is the problem below. Findthe maximum compression and the maximum tension member.
Here is a little help on the solution. The first thing you mustsolve is the forces in the Y direction at A and J. We know that Jy+ Ay = 2000 + 3000 + 5000 by simply adding all external forces inthe Y direction.
Another easy way to solve for Jy and Ay is to do moments aroundany of the elements. Assuming each member has a length of 1 thenthese equations would be;Moment around A: -(1)(2000) – (2)(3000) – 3(4000) + 4(Jy) = 0Moment around J: -(1)(5000) – (2)(3000) – 3(2000) + 4(Ay) = 0
You will find that all of these equations are consistent andwill give you the same Force in Y at A and J
More complex is to do a Force balance at each of the members, Iwill give 2 examples here to help you out. I assume all members arein compression. Under compression the force vectors will alwayspoint towards the node. Positive and Negative signs for the vectorsare simply being in the positive X or Y as assumed.
Forces at DForce at Node D
The forces in the X direction are;F(BD) – F(DF) + cos(60) F(CD) – cos(60) F(DE) = 0F(BD) – F(DF) + 0.5 F(CD) – 0.5 (F(DE) = 0
The forces in the Y direction are;cos(30) F(CD) + cos(30) F(DE) = 00.866 F(CD) + 0.866 F(DE)
Forces at E
Forces in the X directionF(CE) – F(EG) + cos(60) F(DE) – cos(60) F(EF) = 0F(CE) – F(EG) + 0.5 F(DE) – 0.5 F(EF) = 0
Forces in the Y direction– cos(30) F(DE) – cos(30) F(EF) – 3000 = 0-0.866 F(DE) – 0.866 F(EF) – 3000 = 0
Setting up Matrix
I recommend setting up the matrix in Excel as it makes it easierto organize the truss members. here is a spreadsheet with these(without the equations). In setting up the equations you mustinclude the Y equations anywhere where there is an external force(only Y as the equations are only in the Y directions). These nodesare A, C, E, G, J – I recommend simply doing both X and Y at thesenodes. You will have 18 possible equations, but you only need15.
- I Need Help With A Python Assignment About A Truss Problem Assignment 6 Truss To Solve 1 The Truss Problem For This Se 1 (35.84 KiB) Viewed 18 times
- I Need Help With A Python Assignment About A Truss Problem Assignment 6 Truss To Solve 1 The Truss Problem For This Se 2 (23.86 KiB) Viewed 18 times
- I Need Help With A Python Assignment About A Truss Problem Assignment 6 Truss To Solve 1 The Truss Problem For This Se 3 (24.22 KiB) Viewed 18 times
B D 2000 lb E F 3000 lb
C D 2000 lb 60 30 30 E 60 F 3000 lb G