In this example, independent hand calculation results of the internal force values obtained as a result of the earthquake calculation with the mode shapes, periods and mode combination method of a two-storey system with a single span are made and the results of ideCAD Static Structural are compared. The damping ratio used in response spectrum analysis is taken into account as 5%. Full Quadratic Combination (TKB or CQC) has been used as the modal combination method . Independent hand calculation solutions of periods, horizontal displacements and bending moments calculated as a result of modal analysis were made according to Chopra 2012.
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Important Note: The masses are defined only on the beam members for ease of independent manual calculation. |
Comparison of periods
Compared Value | ideCAD |
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Structural | Manual solution | Percentage of error | |
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1st Mode Period | 1.562 | 1.562 | 0% |
2nd Mode Period | 0.5868 | 0.5868 | 0% |
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Comparison of response displacement results
Node and direction | ideCAD |
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Structural | Manual solution | Percentage of error | |
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3 DN (UX) | 7.59 | 7.59 | 0% |
1 DN (UX) | 18.8 | 18.8 | 0% |
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Element end moments comparison (M 33 ) kip-ft
Workman | Node | ideCAD |
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Structural | Manual solution | Percentage of error | ||
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| 3 | 817.99 | 817.99 | 0% |
4 | 817.99 | 817.99 | 0% | |
| one | 433.81 | 433.81 | 0% |
2nd | 433.81 | 433.81 | 0% | |
| 3 | 568.47 | 568.47 | 0% |
5 | 1056.17 | 1056.17 | 0% | |
| one | 433.81 | 433.81 | 0% |
3 | 499.81 | 499.81 | 0% |
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Geometric Properties and System Description
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T 1 = 1.562 s and T 2 = 0.5868 natural vibration periods results were found to be exactly the same with ideCAD StaticStructural. |
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After finding the mode shapes and natural vibration periods, the nodal deformation values for each mode must be found.
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To switch from the horizontal elastic design acceleration spectrum to the displacement spectrum, the following equation is used.
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Information Annex Appendix-4A Detailed Explanation
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Note: In this example, no carrier system response coefficient will be used. Therefore, R y (µ k , T) = 1 and µ k = 1 will be considered. However, in the Design Based on Strength (DOT) approach, the carrier system behavior coefficient is taken into account. |
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The values of u 1st floor = 7.59 in and u 2nd floor = 18.8 are exactly the same as the results of ideCAD StaticStructural. |
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Under the influence of an earthquake (for the X direction) element internal forces can be obtained similarly. The building moment diagram can be drawn in the order described below.
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Elements and end moments are given in the table below when Full Quadratic Joining (TKT or CQC) is applied.
Workman | Node | 1.Mod Moment kip-ft | 2.Mod Moment kip-ft | CQC result kip-ft |
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| 3 |
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| 817.99 |
4 |
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| 817.99 | |
| one |
| 179 | 433.81 |
2nd |
| 179 | 433.81 | |
| 3 | 425 | 374 | 568.47 |
5 | 968 | 412 | 1056.17 | |
| one | 396 |
| 433.81 |
3 | 389 |
| 499.81 |
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Moment values occurring in Ex loading are exactly the same with ideCAD Static Structural results. |
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Important Note: Complete Quadratic Combination (CQC or TKT) or square of the total of the |
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