Statics Truss Problem Involving Method of Sections

In summary, the problem involves determining the forces in members DF and EF, finding the horizontal reaction on the truss at A, and showing that if CF=0, DE=0 also. The crossed members in the traveling bridge crane cannot support compression. The equations ƩM=0, ƩFy=0, and ƩFx=0 are used to solve for the vertical reactions at A and B. The method of sections is necessary to solve the problem, and cutting through four members near E may lead to a solvable solution.
  • #1
shizupple
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Homework Statement


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In the traveling bridge crane shown all crossed members are slender tie rods incapable of supporting compression. Determine the forces in members DF and EF and find the horizontal reaction on the truss at A. Show that if CF=0, DE=0 also.

-Determine force in members DF and EF
-Find the horizontal reaction on the truss at A
-Show that if CF=0, DE=0 also
-Crossed members can't support compression


Homework Equations


ƩM=0
ƩFy=0
ƩFx=0

The Attempt at a Solution


I solved for the vertical reactions at A and B.
ƩMb=0=(1000kN)(24m)+(200kN)(52m)-(Ay)(36m)
Ay= 956kN

ƩFy=0=956kN-1000-200+By
By=244kN

ƩFx=0=Ax-Bx
Ax=Bx

I tried summing moments about E to find the horizontal reactions but they just cancel out.

I know I have to use method of sections to solve but there is nowhere to make a cut that only cuts 3 members. Everywhere I cut except the very bottoms and far left side has at least 4 members to cut through. There isn't even a way to simultaneously solve for a 4 cut and a 3 cut.

Any advise on what to do from here would be greatly appreciated.

Thanks
 
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  • #2
There is at least one cut through 4 members that is solvable because, by inspection, one of the crossed members would be in compression, and therefore ignorable. Hint: somewhere near E...
 

1. How do you identify the free body diagram of a truss in a statics problem?

In order to identify the free body diagram of a truss, you must first isolate the truss from its surroundings. This means removing any external supports or connections and leaving only the truss itself. Then, draw each individual member of the truss as a straight line, noting the direction of the forces acting on each member. Finally, label each force with its corresponding magnitude and direction.

2. What is the method of sections used for in a statics truss problem?

The method of sections is a technique used to solve for unknown forces in a truss by cutting the truss into two sections and applying the equilibrium equations to one of the sections. By doing this, the unknown forces can be solved for without having to solve for every single force in the truss.

3. How do you choose which section to cut in a method of sections problem?

The section should be chosen so that the number of unknown forces is minimized. This means choosing a section where only one or two unknown forces are present, making it easier to solve for those forces using the equilibrium equations.

4. What are the equilibrium equations used in a statics truss problem?

The two equilibrium equations used in a statics truss problem are the sum of forces in the x-direction equals zero and the sum of forces in the y-direction equals zero. These equations ensure that the truss is in a state of static equilibrium, meaning that all forces are balanced and there is no motion.

5. Can the method of sections be used to solve for any unknown force in a truss?

No, the method of sections can only be used to solve for unknown forces that are along the section being cut. If the unknown force is not along the section being cut, another section will need to be chosen or a different method, such as the method of joints, will need to be used.

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