Search
 
 

STATICS - CASE STUDY SOLUTION

    Solve for Truss Reactions


Force Diagram

 

The force in the top member 6-7 needs to be determined when the 1,500 kg car is at joint 2.

First, solve for reactions R1 and R5 by applying both the moment and force equilibrium equations for the whole truss.

     ΣM1 = 0
     -4 (14.72) + 16 R5 = 0
     R5 = 3.68 kN

     ΣFy = 0
     R1 + R5 - 14.72 = 0
     R1 = 11.04 kN

     
    Cut Truss at Required Member


Cut 1 Diagram

 

Since, the member 6-7 needs to be determined, that member must be included in the cut. However, there is is usually more than one location to make a cut.

It is easiest to make a cut where only three or less members are cut. Thus, a vertical cut through members 6-7, 6-3 and 2-3 was done as shown at the left. Notice that there are only three unknowns, which can be solved for with the three equilibrium equations.

     ΣFy = 0
     11.04 - 14.72 - F63 cos45 = 0
     F63 = -5.204 kN

     ΣM1 = 0
     -4 (14.72) - 4cos45 F63 - 4sin45 F63 - 4 F67 = 0
      -58.88 - 2 [(4) (0.7071) ( -5.204)] = 4 F67
     F67 = -7.360 kN  compression

For this cut location, you need to use at least two of the three equilibrium equations. The number of equations may be reduced by other cut locations.

     
    Alternate Cut


Cut 2 Diagram

 

By carefully choosing where the cut is made, the number of calculations can be reduced.

For example, if a cut is made through members 6-7, 3-7, 3-8, and 3-4 it is possible to solve for the member force F67 with one equilibrium equation even though four members are cut.

Since all unknowns, except F67, go through
joint 3, the moment about joint 3 has only one unknown.

     ΣM3 = 0
     -8 (11.04) - 4 F67 + 4 (14.72) = 0
     F67 = -7.360 kN  compression

The solution is identical to the solution for the previous cut.

     
   
 
Practice Homework and Test problems now available in the 'Eng Statics' mobile app
Includes over 500 problems with complete detailed solutions.
Available now at the Google Play Store and Apple App Store.