By Rishabh LalaX Semester

Rajiv Gandhi Proudyogiki VishwavidyalayaIntegrated PG Program

Civil and Structural Engineering

Software Analysis Concepts

Accounts for Shear Behavior

Important when thickness is greater than one tenth of the span

Recommended for more accurate analysis

Should not be used when shear deformation is known to be small.

Thick Vs Thin ShellNeglects transverse

shear deformationWhen deformation is

pure bending, thin shell should be used

Pushover Analysis : Non linear analysis, Loads are considered as static in natureNon Linear Staged Construction Analysis: Non Linear

Analysis, but analysis is done after end of every construction stage

Loads are considered as static in nature, although, they are applied after analysis of previous stage.Linear Static : This is the default settingTime History : For time varying loads Loads are considered as dynamic in

nature

Analysis Type

Two Types :A. Material Non Linearity: Time Dependent Example : Concrete, Frame Hinges

Geometric Non Linearity : P Delta Non Linearity P Delta With large Displacements

Non Linearity

Considering slabs as diaphragms is part of the approximate analysis

Diaphragms distribute horizontal forces to the vertical elements

Rigid diaphragms are assumed to have infinite inplane stiffness

Seismic loading are applied at the center of mass

Used for faster analysis

Rigid Diaphragms

Simulate actual inplane stiffnessBuilding codes favour this Used when there are chances of significant

inplane deformationExample: Slabs with openings, L- or C-shaped

buildings where the ends of the wings can drift independently of each other.

Accidental eccentricity is applied at every node

It is often appropriate to analyze, some stories with rigid and some with semi-rigid diaphragm asumption

Semi- Rigid Diaphragm

Centroid of the stiffness, within the floor diaphragm

Its position is independent of loading magnitude

Its position is different for different storeysIf lateral loads are applied to the rigid

diaphragm, then its position is the one, which does not causes any rotation in that storey.

Center of Rigidity

Equilibrium equations takes into account, the partially deformed shape of the structure also.

Note: Tensile forces tend to resist rotation and compressive forces tend to enhance rotation and destabilize the structure, whereas tensile forces stiffen the structure. This requires moderate iterations.

‘P Delta for large scale displacements’ can be used in case of cables undergoing large displacements. This may require, large amount of iterations to model large displacements and large rotations.

P Delta Displacements

Related to inelastic behaviour of material of the structural component, characterized by force-displacement (F-D) relationship.

Non Linearity of Material

Static non Linear analysis method, where structure is subjected to gravity loading

Results provide insight into ductile capacity of the structural system and indicate the mechanism, load level and deflection at which failure occurs

When analysis frame objects, material non linearity is assigned to discrete hinge locatinos, where plastic rotation occurs

Pushover Analysis

A yield zone with specific inelastic rotation, which forms in a member when plastic moment is reached in a section.

Plastic Moment: When entire cross-section has yielded to bending moment, the moment carrying capacity at that time is called plastic moment.

Plastic Section: Moment carrying capacity of the cross-section

Plastic Hinge

At any cross-section, the plane before bending, remains plane after bending

All tensile stresses are taken up by reinforcement and not by concrete

Tensile stresses may be calculated by F1/(Ac + M.Ast) Where : F1 = Total tension in the member, i.e. pretension in steel before concreting Ac = Cross – section of concrete excluding any finish and excluding steel M = Modular Ratio Ast = Area of cross section of reinforcing steel in tension

Theory of Elasticity

Q = ∑ Pu Du /u(Hu.hs) Where:

∑ Pu = Sum of axial loads on all columns in the story

Du = elastically computed first order lateral deflection

Hu = total lateral force acting within the storyhs = height of story

If Q <= 0.04 no sway columnsIf Q >= 0.004 sway columns

Sway/Non-Sway Column Condition

The most common elastic methods are based on Pigaud’s or Westerguards Theory

The most common limit state theory is based on Johansen’s Yield Line Theory

No actual column can be said to be 100% fixed for all loading conditions and same goes with no actual column can be called 100% hinged

It all depends on the stiffness of the columns and beams and beam column joint.

Common Theory’s

It’s a codal provision based on the assumption that most structures will sustain inelastic deformation.

Also, called “Behaviour Factor”.Depends on :

Capacity of structure to sustain inelastic deformations Energy dissipation capacity Its over strength Stability of its vertical load carrying system during

inelastic deformation Non Linearity of the structure

More the ductility of the structure i.e. more the rotational capacity of the structure, more is the response reduction factor

Response Reduction Factor

This coefficient is based on the spectral response acceleration.

This allows us to design buildings for about 20% of the earthquake forces, by utilizing the flexibility of the structure provided by its ductility. Response reduction factor theory gains its relevance, as most of today’s designs are based on the Earthquake Design Philosophy.

Response Reduction Factor

Elastic : Instant RecoveryInelastic : Very Slow Recovery and might not

be 100% Plastic : No Recovery

Deformation

Evaluation of total response of the building by statistically combining the response of finite number of modes of vibration. A building in general vibrates in many modes and each mode contributes to the base shear and for elastic analysis, this contribution can be determined by multiplying the % of total mass, called effective mass by the acceleration corresponding to that modal period.

Note: The effective mass is the function of lumped mass and deflection at each floor, having largest value for fundamental mode. The mode shapes therefore must be known to compute the effective mass.

Modal Superposition

Modal Analysis is a general procedure for linear analysis of the dynamic response of the structure. Modal Analysis has been widely used in the earthquake resistant design of special structures, such as very tall buildings, dams, etcetera.

However, it has become common for ordinary structures as well, as cost of the high speed computing due to the availability of the not so costly analysis software has come down.

Modal Analysis

Modeling of tall structures to an extent is dependent on the type of analysis done.

The usual approach is to conduct approximate analysis in the preliminary stage and then accurate analysis in the final stage.

Some of the approximations usually done are: 1. Numerous hinges are inserted at points of assumed points

of contraflexure in the beams and columns of a rigid frame to convert the structure into a statically determinate one, from an indeterminate structure.

2.Approximating simple cantiliver instead of a complex bent. 3.If structure is symmetrical, half model analysis is also

acceptableSlabs can be assumed to be diaphragms

Approximate Analysis

Material: Linearly Elastic : This assumption allows for linear methods of analysis

Participating Components : Only primary components participate in overall behavior, ignoring the secondary structural and non-structural components like brick in-fills, heavy cladding, which may have significant effect on the stiffness of the structure.

Floor Slab : Assumed to be rigid in plane. This assumption may fail during narrow and long slab, precast slabs, etcetera.

Cracking : Effects of cracking due to flexural stress are assumed to be represented by reduced moment of inertia of beams by 50% and columns by 80% of the uncracked values.

Modeling Assumptions