Joints to Determine the Forces

Questions:

You must show the application of all the equations of equilibrium and sign convention. Show your final answers on a clear summary diagram. Beauty matters.

Q1.

Fig. 1 is a truss that has a pin support at A and a roller support at D.

Determine:

(a) The support reactions at A and D;

(b) The forces in all members of the truss using the Method of Joints.

Your final results should be shown on a summary diagram.

Fig. 1 

Question 2

Andrea Palladio was one of the most important and famous of the renaissance architects:

 

Not seen by the tourists, but just as important, is what was holding everything up. One of

Palladio’s contributions was his extensive use of what is called the Palladian truss, examples of which were used in the Ponte Vecchio in Italy:

 

The Palladian truss shown in Fig. 2 has a pin support at A and a roller support at G. Determine:

(a) The support reactions at A and G;

(b) Use the Method of Joints to determine the forces in members AB, AH, BC, and BH.

Show the results of your analysis on a summary diagram.

Fig. 2 

Question 3

The structure shown in Fig. 3 is a hybrid rigid beam member ABC being supported by a truss.

There is a pin support at D and at E.

(a) Determine the support reactions at D and E.

(b) Now use Method of Joints to determine the forces in members CD, CE, and EF.

(c) Use the Method of Sections and a free-body diagram of ABC, determine bar forces CF, BG, and AG.

(d) Finish the analysis by determining the force in member FG using any method you choose.

(e) Show your final results on a summary diagram.

Fig. 3

Q4.

It is sometimes the case that we can use the Method of Sections to solve for members in a truss without first calculating the support reactions. Given the truss in Fig. 4:

  • Determine the force in members BC, BE, EFusing the Method of Sections. If possible, solve for these forces without first getting the support reactions.
  • Given your analysis, how will the forces in BC, BE, EFchange if the applied load at B increases from 4 kN to 10 kN (Note: You should be able to answer this without any further calculations! Provide a sentence or two of explanation with reference to a freebody diagram).
  • Draw your answers for Part (a) on a sketch of the sectioned truss.

Fig. 4

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