Structural Dynamics of Earthquake Engineering: Theory and Application Using Mathematica and Matlab 1st. Edition by Sekaran Rajasekaran | 9781845695187 | 1845695186 | Holooly

Mechanics Dynamics

Structural Dynamics of Earthquake Engineering: Theory and Application Using Mathematica and Matlab

141 SOLVED PROBLEMS

Question: 17.3

A 4 m long vertical cantilever 100 mm internal diameter steel pipe supports 25 kN weight attached on the top as shown in Fig. 17.16a. Do = 115 mm, Di = 100 mm, I = 3.676 × 10^6 mm^4 E = 200 × 10^6 kN/m². Determine the peak deflection; bending stress due to El, Centro ground motion. ...

Verified Answer:

k=\frac{3 I}{l^3}~ E[/late...

Question: 17.4

A single storey reinforced concrete (RC) building (see Fig. 17.17a) is idealized for this purpose of structural analysis as a mass-less frame supporting a dead load (DL) of 50 kN on the beam level. The frame is 8 m wide and 4 m high. Each column and beam have a 250 mm square section. Assuming ρ = 5 ...

Verified Answer:

I=\frac{1}{12} \times 250^4=3.256 \times 10...

Question: 17.5

The frame shown in Fig. 17.18 is for use in a building to be located on sloping ground. The beams are made much stiffer than columns and can be assumed to be rigid. The cross-section of the columns is 250 mm square but their lengths are 4 m and 8 m respectively. Determine the base shear in the two ...

Verified Answer:

Since the beam is rigid, the stiffness of columns ...

Question: 17.6

Construct a Newmark–Hall design spectrum for a maximum ground acceleration equal to that of Northridge earthquake 0.308g and for concrete buildings. ...

Verified Answer:

(a) Determine maximum ground motion parameters Max...

Question: 17.7

Consider an elastic design spectrum, 84.1% for ground motion ug0 = 1g; ug0 = 121.92 cm/s; ug0 = 91.44 cm; ρ = 5%. Using the program developed it is possible to construct a design spectrum as shown in Fig. 17.23. ...

Verified Answer:

From Fig. 17.23, we can construct a pseudo-acceler...

Question: 17.8

Estimate the maximum sensitive response for the industrial building of Example 17.1 using Newmark–Hall design spectra for an anticipated ground acceleration of 0.308g and for a damping factor of 0.05. Compare the results with the maximum response obtained from time history analysis. ...

Verified Answer:

Damping = 5% (i) NS direction, T = 0.567 s From ch...

Question: 17.9

Construct Newmark–Hall broad-banded design spectrum for a site. Develop spectrum curves using the program for damping factors 0.02, 0.05, 0.1. Estimate the maximum horizontal ground displacement assuming the maximum ground acceleration = 0.4 g, assuming group L and 84.1% on 50 m alluvium by bed ...

Verified Answer:

Maximum ground acceleration = 0.4g = 0.4 × 981 cm/...

Question: 17.2

Construct response spectra for the NS component of E1 Centro earthquake (see Fig. 17.5a). Consider damping factors 0, 0.02, 0.05, 0.1 and 0.2. ...

Verified Answer:

The spectral displacement

S_{d}

, sp...

Question: 18.13

A uniform two span continuous bridge shown in Fig. 18.35 with flexural stiffness EI idealized as lumped mass. Let us formulate the equation of motion subjected to vertical motion at 1, 2, 3 as ug1, ug2, ug3 at supports. ...

Verified Answer:

Formulation stiffness matrix 10 × 10. Assuming tra...

Question: 18.11

Determine the effective modal mass and the effective modal height for the frame shown in Fig. 18.29. ...

Verified Answer:

The modal distribution of effective earthquake for...

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