This set of Earthquake Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Analysis for Multi-Support Excitation”.

1. When are the spatial variations of ground motions considered during modelling and analysis of a structure?

a) If the plan dimensions of structure are very large and comparable to seismic wavelengths

b) If the plan dimensions of structure are very small and not comparable to seismic wavelengths

c) If the height of structure is very large and comparable to the seismic wavelength

d) If the weight of the structure is very large

View Answer

Explanation: The implications of spatial variation of ground motions are not obvious when the plan dimensions of the structure are very small in comparison with the wavelengths of the seismic waves. For large plan dimensions, the ground motion is not same at all the points on foundation base and thus spatial variation is considered.

2. What is the reason behind differential support motions during earthquake?

a) For light structures, the variation of ground motion is different from one point to another

b) For heavy structures, the behavior of the structure is different at different locations

c) For tall structures, the sway motion induces differential support motions

d) For long span structures, the variation of ground motion is different from one point to another point

View Answer

Explanation: For long span structures, the seismic wavelengths are comparable to plan dimension of structure and so motion on different point of structure may be different. These structures must be analyzed considering the spatial variations as well.

3. Why does the failure due to inadequacy of bearing seating length to accommodate out of phase motions at different support points occur in long bridges?

a) The weight of the structure is not accurately calculated

b) The spatial variations of the ground motions are not considered

c) The loads due to movement of vehicles is not considered

d) The uplift forces from the soil are not considered

View Answer

Explanation: Long span structures like bridges should be designed to survive this additional distress, which is caused entirely due to non-uniform nature of earthquake ground motions. Not considering this aspect while designing the seating length of bearing pads has led to failure of bridges in the past.

4. Why is the equation of motion specified in terms of ground acceleration only and not in ground displacement and velocity?

a) It is easier to solve the equation of motion in terms of ground acceleration

b) Ground Displacements and Velocities are complex quantities and thus acceleration is preferred

c) Equation in terms of ground acceleration easily programmable

d) Ground velocities and displacement are generally not available and when available their values are questionable due to many assumptions

View Answer

Explanation: The ground velocities are displacements are not available generally. When they are available, the reliability of those values is doubtful due to assumptions necessary during calculation velocity and displacement from acceleration.

5. What is the equation of motion for multi support excitation and spatial variation?

a) Mü + Cü + Ku = -[Mr+M_{g}]ü_{g}

b) Mü + Cu̇ + Ku = f

c) Mü + Cu̇ + Ku = -Mrü_{g}

d) Mü + Cü + Ku = [Mr+M_{g}]ü_{g}

View Answer

Explanation: This is the equation of motion for multi support excitation when considering spatial variation. This equation can be solved for dynamic component of the response by any standard procedure of dynamic analysis, such as the mode superposition method.

6. Responses of all degrees of freedom due to a unit displacement of a support point is represented by which of the following?

a) Influence stiffness matrix

b) Response coefficient matrix

c) Influence coefficient matrix

d) Response freedom matrix

View Answer

Explanation: The influence coefficient matrix contains the responses of all degrees of freedom caused by a unit displacement of a support point. It is denoted by R and it is given by R = -K

^{-1}K

_{g}. This matrix is used to find out the quasi-static displacements.

7. Spatial variation of earthquake ground motion is inconsequential for a long span structure.

a) False

b) True

View Answer

Explanation: Spatial variation of earthquake ground motion is significant for long-span structures like bridges and pipelines. It is inconsequential for short span structures like an elevated reservoir where the motion can be assumed to be uniform at all points on the foundation base for all practical purposes.

**Sanfoundry Global Education & Learning Series – Earthquake Engineering.**

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