Dynamic Analysis of Structures Questions and Answers

Q: The fundamental period of a building is most sensitive to

Correct answer: its mass and lateral stiffnessThe period is \( 2\pi\sqrt{m/k} \), so mass and lateral stiffness are the only quantities that enter it.Everything that matters does so through one of them: height and framing through the stiffness, floor construction and imposed load through the mass. The concrete grade in the slabs affects the period only through the small change it makes to the frame's stiffness, and finishes and occupants affect it only as mass - the option naming both parameters directly is the answer.

91.

The equation of motion is written about the static equilibrium position so that

A.damping may be neglected without loss of accuracy
B.the stiffness becomes independent of the displacement
C.the self weight and its initial deflection drop out of the equation
D.the mass of the structure need not be considered at all

Answer: C

Correct answer: the self weight and its initial deflection drop out of the equation

Measuring displacement from the position the structure already occupies under its own weight makes the weight and the corresponding spring force cancel exactly, since they balance in that position.

What remains is the equation in terms of the dynamic displacement alone, and the response computed is the movement about the static position - which is what matters for stresses caused by the vibration. Damping, stiffness and mass all remain in the equation unchanged.

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92.

A structure is described as rigid in dynamic terms when its natural period is

A.very much longer than the period of the excitation
B.exactly equal to the period of the excitation
C.impossible to compute from the model
D.very much shorter than the period of the excitation

Answer: D

Correct answer: very much shorter than the period of the excitation

A structure whose period is far shorter than the excitation's cannot flex appreciably during a cycle of the loading. It simply follows the ground, moving with it as a rigid body, and its acceleration equals the ground acceleration.

That is the short-period end of a response spectrum, where the spectral acceleration tends to the peak ground acceleration. A structure with a much longer period behaves the other way: the mass barely moves while the base does, which is the principle base isolation exploits.

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93.

The fundamental period of a building is most sensitive to

A.its mass and lateral stiffness
B.the grade of concrete used in its slabs
C.the colour and type of its external finishes
D.the number of occupants present at the time

Answer: A

Correct answer: its mass and lateral stiffness

The period is \( 2\pi\sqrt{m/k} \), so mass and lateral stiffness are the only quantities that enter it.

Everything that matters does so through one of them: height and framing through the stiffness, floor construction and imposed load through the mass. The concrete grade in the slabs affects the period only through the small change it makes to the frame's stiffness, and finishes and occupants affect it only as mass - the option naming both parameters directly is the answer.

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94.

Empirical code formulae for the fundamental period of a building are usually written in terms of

A.the importance factor assigned to the building
B.the height of the building and its structural system
C.the compressive strength of the concrete alone
D.the seismic zone in which the building stands

Answer: B

Height stands in for the mass and stiffness that are not yet known at the outset of a design, with a different expression for framed and for braced or walled systems. The zone and importance factors affect demand, not period.

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