Structural dynamics

Table of Contents
Introduction 2
1. Response spectrum analysis 3
1.1 Design Acceleration Response spectrum 3
1.2 Fundamental period of the building 6
1.3 Mass of the building 8
1.4 Calculation of base shear 11
1.5 Distribution of base shear 12
2. Conceptual design 14
2.1 Importance of conceptual design 14
3. LUSAS model 15
3.1 Initial mathematical model 15
Shear force diagrams – x-direction (fy) 16
Shear force diagrams – Y-direction (fZ) 17
Bending moment diagrams – x-direction (MZ) 18
Bending moment diagrams – y-direction (My) 19
Reactions (fx) 20
3.2 Running the earthquake 21
Eigenvalues 22
Shear force diagrams 23
Bending moment diagrams 24
Displacement 25
3.3 Second model – static analysis 26
Shear force diagrams – x-direction (fy) 27
Shear force diagrams – z-direction (fz) 28
Bending moment diagrams – x-direction (mz) 29
Bending moment diagrams – y-direction (my) 30
Displacement 31
Reactions 31
3.4 Second model – dynamic analysis 32
Shear force diagrams 32
Bending moment diagrams 33
Displacement 34
4. Reflection of analysis and conceptual design 35

Introduction
This report will look at conceptual design for earthquake resisting structures. It will look in depth at a specific structure under a calculated earthquake. The structure will be created as a model using LUSAS modeling software and analyzed to show the building’s behavior under static and dynamic loadings. After an initial model has been created and analyzed, changes will be made to it and re-evaluated to show how changes to the structure cause it to behave differently.
The structure to be analyzed initially has the following dimensions.

Appendix A shows the plan view and section views for the initial model and appendix B shows the plan view and section views for the second model.

1. Response spectrum analysis
1.1 Design Acceleration Response spectrum

a - (Seismic ground acceleration)
0.24g
A - (Maximum horizontal seismic ground acceleration)
2.3544
ϒI – (Importance coefficient)
1.2
q –