Author :

Posted On :
The masses of N stories are lumped at these levels with mj denoting the mass at the jth floor.

**Lumped mass
system: shear building **

Consider the shear building shown
in Fig. 18.1 subjected to earthquake excitations. The masses of *N*
stories are lumped at these levels with *m _{j}* denoting the mass
at the

We assume floor displacement
relative to the ground can be expressed as

Where *z* and *ψ* are the displacement of the roof
and shape function respectively.

Hence total displacement

1 Equation of
motion

Shear *V _{j}* in the

*V _{j}
*=

= *k _{j}
*∆

*k _{j}*(

*k _{j}*, the
storey stiffness, is the sum of all lateral stiffness of all columns to that

where *EI* is the flexural rigidity of the
column and *h* is the storey height. At each time instant the system is in
equilibrium under the action of

internal storey shear and inertia
force and using D’Alembert’s principle we get

Using the principle of virtual
displacement to formulate equilibrium equation, the external virtual work can
be written as

The internal virtual work is due
to storey shear *Vj*(*t*) acting through storey drifts

Now we can express displacement
in terms of generalized coordinates as

where ∆* _{j}*, the
stories drift given in terms of storey displacements (see Fig. 18.2), {

Consider a three storey frame
shown in Fig. 18.3. It can be proved,

2 Response
analysis

where *h* is the height of
the floor above base. In particular the shear and over-turning moment at the
base are

Example 18.1

The uniform five storey shear
frame with rigid beams shown in Fig. 18.4 is subjected to ground acceleration.
All the floor masses are *m* and all stories have same height and
stiffness *k*. Assume the displacement to increase linearly with height
above base; formulate the equation of motion for the system and determine
natural frequency.

Example 18.2

Determine the peak displacement,
storey shears, floor overturning moment for the above frame with *m* = 45
412 kg, *k* = 5530 kN/m; *h* = 3.657 m due to ground motion
characterized by design spectrum scaled to peak ground acceleration of 0.25*g*.
The spectrum is given in Fig. 18.5.

Example 18.3

Solve Example 18.1 using a normalized vector *φ* instead of *ψ*.

The results obtained are the same as the ones
obtained in Example 18.2

Tags : Civil - Structural dynamics of earthquake engineering

Last 30 days 34 views
Related words : ### What is Lumped mass system: shear building Define Lumped mass system: shear building Definition of Lumped mass system: shear building where how
meaning of Lumped mass system: shear building
lecturing notes for Lumped mass system: shear building lecture notes question and answer for Lumped mass system: shear building answer
Lumped mass system: shear building study material Lumped mass system: shear building assignment Lumped mass system: shear building reference description of Lumped mass system: shear building
explanation of Lumped mass system: shear building brief detail of Lumped mass system: shear building easy explanation solution Lumped mass system: shear building wiki
Lumped mass system: shear building wikipedia how why is who were when is when did where did Lumped mass system: shear building list of Lumped mass system: shear building school assignment college assignment
Lumped mass system: shear building college notes school notes kids with diagram or figure or image difference between Lumped mass system: shear building www.readorrefer.in - Read Or Refer

Recent New Topics :
| Valuation of Bonds and Shares | | Need of Labour welfare | | Getting it Right at Mcdonalds | | Strategic Issues | | Important Short Questions and Answers: Strategies | | Strategies | | Strategy and Process | | Effective Management of small Business | | Growth strategies in small business | | Production and Operation Management - Small Business | | Human Resource Mobilization | | Important Short Questions and Answers: Business Plan Preparation | | Feasibility Report Preparation and Evaluative Criteria | | Budgeting Project Profile Preparation | | Ownership Structure and Capital - Business Plan Preparation | | Criteria for Selection Process - Business Plan Preparation | | Business Pre-feasibility Studies | | Sources of Product for Business | | Business Plan Preparation | | Important Short Questions and Answers: Developing the Winning Edge | | Developing the Winning Edge | | Managerial Styles | | Competition - Managerial Effectiveness | | Job Challenge | | Group Influences |