A fink truss is shown below.

Question

A fink truss is shown below.

1. Determine the magnitude of the resultant. 
2. Determine the horizontal distance of the resultant from the hinge support. 
3. Determine the reaction at A. 
4. Determine the reaction at B. 

-Type in your answer/s rounded off to 2 decimal places except for whole numbers. (ex: 10.67, 28, 732.40)

-If your answer is 120.00 kN, just write 120 kN

-Do not round off values during solving. Use the store function of your calculator or its fraction if applicable.

-Include the units after your answer. Leave a space between the value and the unit. (ex: 6323.17 m, 73.10 rad/s^2, 100 kN)

Answer 1

I'm going to have to make an assumption about this truss in order to make my answer seem reasonable. Perhaps Luke can offer more guidance if he knows more about Fink Trusses.

My assumption is that the two diagonal beams with 1335N are joined perpendicular to the upper beams. Without this assumption, I cannot figure any way to solve the problem, and it seems reasonable that they would be perpendicular in this case. The math is easy if they are perpendicular, and impossible if they aren't.

In this case, then you have some 30 60 90 triangles on the left and right hand sides of the truss, and an equilateral triangle right in the middle.

Part 1) The resultant force should just be the sum of all labeled forces, and pointing in the downward direction. Since all the forces are parallel and pointing downward, you can just add the forces together as scalar quanitites. F_resultant = 15130N

Part 2) Technically you'll need to know which support you are referencing, but for now let's do the math in reference from the left support.

distance from left support = [ ∑(F_applied * distance from left support) ] / F_resultant

This is similar to finding the center of mass, but we're finding the "center of force." You multiply each force by its distance from the center, and then divide by the total resultant force. This leaves you with something like the "equivalent distance a single force should be applied."

distance from left support = [(890*0 + 1335*2.25 + 8900*3 + 1780*4.5 + 1335*6.75 + 890*9)] / (15130)

distance from left support = 3.617647059 meters. This is reasonable, since without the 8900N force, the load would be evenly balanced at 4.5m, so we'd expect it should be a little further to the left than that.

(by the way, to get the 2.25 for the two forces with 1335N, you have to know about your 30 60 90 triangles, if you know the hypotenuse, then you can find the lengths of other sides.)

Running out of time for parts 3/4, but you can set up a torque equation in both cases to determine the force that the supports A and B must uphold. To find the weight of the load at A, just make B the fulcurum and vice versa.