4 parallel-chord truss. 3. Demonstrate your procedure on an example ft. 5 k 5 k 5 k 5 k. 6 ft

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1 CE 331, Spring 2005 Beam nalogy for Truss Design: 1 / 6 We need to mae several decisions when designing a truss. First, we need to choose a truss shape. Then we need to determine the height of the truss. nd finally we need to determine the member sizes. lthough we will liely use a computer program to chec our design, we need to mae initial estimates for our first analysis. We can mae better decisions about truss design if we understand the patterns of internal forces (bar forces) caused by the external loads on trusses. The "beam analogy" is a tool that helps us understand how forces are distributed through a truss. The beam analogy produces exact results for parallel chord trusses (horizontal top and bottom chords) but is still useful for understanding the behavior of other types of trusses. In this exercise, you will derive the simple equations and procedures for using the beam analogy by woring through an example. You will perform the following steps: page 1. Calculate the average chord and diagonal forces in each panel using statics Write a procedure to calculate the maximum average chord force in a 4 parallel-chord truss. 3. Demonstrate your procedure on an example. 5 Example: 5-panel parallel-chord truss. The truss dimensions and loads are shown below. 8 ft B C 6 ft B C

2 CE 331, Spring 2005 Beam nalogy for Truss Design: 2 / 6 1. Calculate the average magnitude of the chord forces (f ch_avg ) and the average magnitude of the diagonal forces (f diag_avg ) in each panel indicated below. 4 ft Mid-Panel #1. Cut the truss at Section - (see figure on f top previous page). a f1 Chord Forces: Sum moments about Point a where the diagonals cross. ssume the chord forces are about equal magnitude. Then the top chord must be in compression (as indicated in the figure at right) and the bottom chord must be in tension (as indicated) to resist the moment caused by the reaction about point a. 6 ft 10 f2 fbot FBD for Section - f ch_avg = Diagonal Forces: Sum forces in the vertical direction. ssume the diagonal forces are about equal magnitude. Then f 1 must be downward (as indicated in the setch) and f 2 must be upward (as indicated) to resist the reaction f diag_avg =

3 CE 331, Spring 2005 Beam nalogy for Truss Design: 3 / 6 Mid-Panel #2: Cut the truss at Section B-B. Chord Forces: Same procedure as for Mid-Panel #1. 5 a f top f1 f2 fbot 10 FBD for Section B-B f ch_avg = Diagonal Forces: Same procedure as for Mid-Panel #1. f diag_avg = Mid-Panel #3: Cut the truss at Section C-C. Chord Forces: Same procedure as for Mid-Panel # a f top f1 f2 fbot 10 FBD for Section C-C f ch_avg = Diagonal Forces: Same procedure as for Mid-Panel #1. f diag_avg =

4 CE 331, Spring 2005 Beam nalogy for Truss Design: 4 / 6 2. Set up equations to calculate the maximum average chord force and the maximum average diagonal forces. (a) Review the calculations of the average chord forces at the middle of Panels 1, 2 and 3 above. For a typical calculation, separate the terms involving the loads and reactions from the terms involving the chord forces. Call the first set of terms M ext (the net moment about a due to external forces; and call the second set of terms M int (the net moment about a due to internal forces). (b) What is an expedient way to calculate the maximum M ext? (c) Write an equation relating the average chord force (f ch_avg ) and the moment due to internal forces (M int ). (d) Review the calculations of the average diagonal forces at the middle of Panels 1, 2 and 3 above. For a typical calculation, separate the terms involving the loads and reactions from the terms involving the diagonal forces. Call the first set of terms V ext (the net shear force due to external forces); and call the second set of terms V ext (the net shear force due to internal forces). (e) What is an expedient way to calculate the maximum V ext?

5 CE 331, Spring 2005 Beam nalogy for Truss Design: 5 / 6 (f) Write an equation relating the average diagonal force (f diag_avg ) and the shear force due to internal forces (V int ). (g) Use the results above to write a procedure to calculate the maximum average chord force and maximum average diagonal force for a parallel-chord truss.

6 CE 331, Spring 2005 Beam nalogy for Truss Design: 6 / 6 3. Demonstrate your procedure for the truss shown below. Calculate the maximum average chord force (for the panel with the maximum magnitude average chord force) and the maximum average diagonal force (for the panel with the maximum magnitude average diagonal force). 10 ft B C 8' B C nswers: max f ch_avg = max f diag_avg = 20.0