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1
- #1
aligorsi
Structural
- Apr 28, 2016
- 8
This is continuation of the conversation started in a previous thread (thread507-475991).
I was unable to work on the topic for a while since I was busy with some projects, however, after getting some time I went through all the comments and came up with a solution. I just wanted to post my conclusion in case someone else had a similar issue.
I prepared 2 excel sheets for 2 separate cases.
1. Sinusoidal load applied on a simply supported beam.
2. Sinusoidal load applied on a 2d floor system.
For the first case, I used the equations in "FORCED VIBRATION WITH VISCOUS DAMPING" section of shock and vibration handbook by Cyril M. Harris.
Step 1: Calculate natural frequency of simply supported beam using fn = (pi/2)*SQRT((gEI)/(QL^4))
Step 2: I calculated values of Rd and ϴ from equation 2.33 of the handbook.
Step 3: The ratio of peak acceleration to gravity was calculated by dividing the equation for acceleration (equation 2.37) by g.
For the second case, I used a combination of AISC Design guide 11 and equations used in the first case.
Step 1: calculate natural frequency of joists and girders individually treating them as simply supported beams.
Step 2: calculate natural frequency of the floor system as a whole using equation 3.2 of the design guide.
Step 3: After this Steps 2 and 3 were followed as per the first case
I have attached both excel sheets as well. Please feel free to review the calculations and give your comments.
I was unable to work on the topic for a while since I was busy with some projects, however, after getting some time I went through all the comments and came up with a solution. I just wanted to post my conclusion in case someone else had a similar issue.
I prepared 2 excel sheets for 2 separate cases.
1. Sinusoidal load applied on a simply supported beam.
2. Sinusoidal load applied on a 2d floor system.
For the first case, I used the equations in "FORCED VIBRATION WITH VISCOUS DAMPING" section of shock and vibration handbook by Cyril M. Harris.
Step 1: Calculate natural frequency of simply supported beam using fn = (pi/2)*SQRT((gEI)/(QL^4))
Step 2: I calculated values of Rd and ϴ from equation 2.33 of the handbook.
Step 3: The ratio of peak acceleration to gravity was calculated by dividing the equation for acceleration (equation 2.37) by g.
For the second case, I used a combination of AISC Design guide 11 and equations used in the first case.
Step 1: calculate natural frequency of joists and girders individually treating them as simply supported beams.
Step 2: calculate natural frequency of the floor system as a whole using equation 3.2 of the design guide.
Step 3: After this Steps 2 and 3 were followed as per the first case
I have attached both excel sheets as well. Please feel free to review the calculations and give your comments.
