𝐖𝐡𝐲 𝐚𝐫𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐚𝐥 𝐟𝐨𝐫𝐜𝐞𝐬 𝐢𝐧 𝐬𝐡𝐞𝐚𝐫 𝐰𝐚𝐥𝐥𝐬 𝐟𝐫𝐨𝐦 𝟑𝐃 𝐫𝐞𝐬𝐩𝐨𝐧𝐬𝐞 𝐬𝐩𝐞𝐜𝐭𝐫𝐮𝐦 𝐚𝐧𝐚𝐥𝐲𝐬𝐢𝐬 𝐦𝐮𝐜𝐡 𝐥𝐨𝐰𝐞𝐫 𝐭𝐡𝐚𝐧 𝐟𝐫𝐨𝐦 𝐡𝐚𝐧𝐝 𝐜𝐚𝐥𝐜𝐮𝐥𝐚𝐭𝐢𝐨𝐧?

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That topic keeps coming up from engineers who are starting to use #3Dseismicanalysis for buildings. Inevitably, a student asked me that very question just a couple of weeks ago…

FEA users are always encouraged to first carry out a simple #handcalculation before running a complex 3D analysis. One should always have beforehand a rough idea of the results that the 3D model should produce. And, most importantly, when there are differences, 𝐨𝐧𝐞 𝐬𝐡𝐨𝐮𝐥𝐝 𝐛𝐞 𝐚𝐛𝐥𝐞 𝐭𝐨 𝐞𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞𝐦.

There are three main causes of differences in results between a hand calculation using #EquivalentLateralForces (#ELF) and a 3D spectral analysis using the #ResponseSpectrumMethod (#RSM).

👉 First, the mass considered for the calculation of the seismic force is 𝐧𝐨𝐭 𝐭𝐡𝐞 𝐬𝐚𝐦𝐞 in the two methods. In ELF, the #totalmass of the structure is considered. In RSM, the #effectivemass is considered separately for each significant mode, and results are then combined using, for instance, the SRSS method. Consequently, the resulting total seismic force is usually lower for RSM than for ELF.

👉 Second, the fundamental period may be different depending on the model that is used, which can lead to different values of spectral acceleration. Moreover, in RSM, each mode may have a 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝐬𝐩𝐞𝐜𝐭𝐫𝐚𝐥 𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧. Please note that this point can either increase or decrease the overall effect of the seismic action.

👉 Last but not least, the typical approach for hand calculation of shear resisting systems consisting of shear walls neglects #frameeffects. In contrast, 3D models consider these effects unless specific measures are taken. As a result, the hand calculation produces only shear forces and bending moments in the shear walls; however, in the 3D analysis, #axialforces also typically appear. Consequently, a significant portion of the overall seismic overturning moment can be supported by the lever arm of these axial forces. Additionally, non shear-resisting supporting members can contribute in a similar manner

🔑 Each of the three causes above can lead to significant discrepancies when comparing simplified ELF and 3D RSM approaches. The question for each of them is then if it is an effect that 𝐢𝐬 𝐝𝐞𝐬𝐢𝐫𝐞𝐝 𝐨𝐫 𝐧𝐨𝐭. If it is desired, then the difference must be accepted or, if possible, the simplified approach must be refined to better validate the 3D analysis. If it is not desired, then the 3D model must be adjusted. Please note: the #validation of the 3D model and its adjustment is a step that must be carried out for any complex analysis – seismic or not.

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