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Sci Tech
Earthquake resistant design, construction
EARTHQUAKE CAUSES shaking of the ground. So a building resting on it will experience motion at its base. From Newton's First Law of Motion, even though the base of the building moves with the ground, the roof has a tendency to stay in its original position.
But since the walls and columns are connected to it, they drag the roof along. This is like the situation that you are faced with when the bus you are standing in suddenly starts; your feet move with the bus, but your upper body tends to stay back making you fall backwards!!
This tendency to continue to remain in the previous position is known as inertia. In the building we construct, since the walls or columns are quiet flexible, the motion of the roof is different from that of the ground.
Consider a building whose roof is supported on columns. Coming back to the analogy of yourself on the bus: when the bus suddenly starts, you are thrown backwards as if someone has applied a force on the upper body. Similarly, when the ground moves, even the building is thrown backwards, and the roof experiences a force, called inertia force.
If the roof has a mass M and experiences an acceleration of a, then from Newton's Second Law of Motion, the inertia force FI is mass M times acceleration a, and its direction is opposite to that of the acceleration. Clearly, more mass means higher inertia force. Therefore, lighter buildings sustain the earthquake shaking better.
Effect of deformations in structures
The inertia force experienced by the roof is transferred to the ground via the columns, causing forces in columns. These forces generated in the columns can also be understood in another way.
During earthquake shaking, the columns undergo relative movement between their ends. This movement is shown as quantity u between the roof and the ground. But, given a free option, columns would like to come back to the straight vertical position, i.e., columns resist deformations.
In the straight vertical position, the columns carry no horizontal earthquake force through them. But, when forced to bend, they develop internal forces. The more is the relative horizontal displacement u between the top and bottom of the column, larger is this internal force in columns.
Also, the stiffer the columns are (i.e., bigger is the column size), larger is this force. For this reason, these internal forces in the columns are called stiffness forces. In fact, the stiffness force in a column is the column stiffness times the relative displacement between its ends.
Sponsored by Building Materials and Technology Promotion Council, New Delhi, India.
C. V. R. Murthy
IIT, Kanpur
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