[Literature Review: Estimating Natural Frequency of Building]

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Literature Review: Estimating Natural Frequency of Building

Natural Frequencies of Structure

Introduction

A common technique for analyzing structures is to treat them as lumped masses on a single rod. The vertical elements in the building (i.e., columns) provide resistance to lateral movement. Most of the weight on the building (i.e., furniture, occupants, floor system) is located at each story level. The rod can be thought of as the columns in the building, and the lumped masses represent the weights applied at each story level. (Bolton, 1978)A single story building would be shown with a rod representing the height of the structure, with the entire weight of the structure located at the top. A five story building, as shown below, would have a rod extending for five stories (columns idealized as a single column) with the weights attached at each of the five floor levels.

Two important considerations in this model is the mass of the structure (note: weight = mass x gravity) and the stiffness. The stiffness of a structure corresponds to how well it will resist a force being applied to it. In earthquake design, the outside force is the ground motion which ends up forcing the structure to move side to side (horizontal force). Therefore, the walls of the building end up being the contributing factor for the stiffness. (Bolton, 1978)

The stiffness is determined by four parameters, the length, material properties, moment of inertia (I), and boundary conditions (how the member is attached at its ends). The material property is called the modulus of elasticity (E) and can be thought of as how well the building material can resist force without bending. The two most common materials are steel and concrete. Steel is about eight times stiffer than concrete, so its modulus of elasticity is eight times larger than concrete. The moment of inertia can be thought of as how much material there is. This makes sense because a larger wall will end up being stiffer than a smaller wall of the same material.

The stiffness and the mass of the building, therefore, control how the building will respond to an earthquake. An interesting response to an earthquake is when a structure vibrates at its natural frequency. Frequency is how many times per second something will move back and forth. For example, if you stretch a spring it will not only bounce back to its original position, but it will also overshoot this position and end up stretching back the other way. When it gets to the end of that side it will repeat the process bouncing back in the other direction. This is similar to what an earthquake does to a building because during an earthquake the ground moves back and forth, which is like stretching the spring in one direction and then moving it back to the other repeatedly.

The natural frequency is a special rate of moving back and forth. At this frequency the building will shake uncontrollably. This is especially damaging during an earthquake ...