PDF Finite Element Analysis and Design of RC Buildings

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Seminar on

Finite Element Analysis and Design of RC Buildings

25-26

^th

May 2005

Multi Media Theater, UNIMAS Main Campus Kota Samarahan, Sarawak, Malaysia

Organized By

Asian Center for Engineering Computations and Software , School of Civil Engineering, Asian Institute of Technology (AIT)

Bangkok, Thailand

JOintly organized by

Department of Civil Engineering, Faculty of Engineering University Malaysia Sarawak

The Institution of Engineers, Malaysia

Sarawak Branch

(2)

Dr. Naveed Anwar ~

Asian Institute of Technology, AIT ~

Finite Element Analysis and Design of RC Buildings'

May 25-26, 2005

Multi Media Theater, UNIMAS Main Campus Kota Samarahan, Sarawak

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[ Outline

• Overview of Computer Aided Analysis and Design of Buildings

• Structural Systems: Types, Selection and Behavior

• Modeling and Analysis of Buildings in 3D

• Design of Gravity Load Resisting Systems

• Design of Lateral Load Resisting Systems

• Special Modeling Techniques for Shear Walls, Transfer Girders, Deep Beams, Foundation Systems and Long Columns

• Analysis, Design and Detailing of Foundations

• Dynamic and Non-linear Analysis for Wind and Earthquake Loads

• Pushover Analysis for Performance Based Design

• Staged Construction Analysis

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. . ACECOMS

ASian Institute of Technology, AIT

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[ Building Systems

• Building is an assemblage of various Systems - Basic Functional System

- Structural System - HVAC System

- Plumbing and Drainage System

- Electrical, Electronic and Communication System - Security System

- Other specialized systems

Finite Element Analysis and Design of RC Buildings - 2

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...

Dr. Naveed Anwar ^~

Asian Institute of Technology, AIT

~

The Building Structural System · Physical

Diaphragm Frame and Shear Walls

Floor Slab System Lateral Load Resisting System

Gravity Load Resisting System

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,

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The Building Structural System· Conceptual

• The Gravity load Resisting System (GLRS)

- The structural system (beams, slab, girders, columns, etc) that act primarily to support the gravity or vertical loads

• The Lateral Load Resisting System (LLRS)

- The structural system (columns, shear walls, bracing, etc) that primarily acts to resist the lateral loads

• The Floor Diaphragm (FD)

- The structural system that transfers lateral loads to the lateral load resisting system and provides in-plane floor stiffness

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. . ACECOMS

ASian Institute of Technology, AIT

_

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[r----st~r~tural System - Analysis Model

STRUCTURE

RESPONSES

EXCITATION

Displacements Loads

~ Strains

Vibrations

~ ^Stress

Settlements

Stress Resultants Thermal Changes

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Structural Model

Finite Element Analysis and Design of RC Buildings - 4

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Dr. Naveed Anwar

Asian Institute of Technology, All

~

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[ The Structural System

STRUCTURE

EXCITATION

..

_P.⁶

¢

^RESPONSES

• Linear

• Static • Elastic

• Dynamic • Inelastic • Nonlinear

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[ Analysis of Structures

P. Real Structure is governed by

"Partial Differential Equations" of various order

Direct solution is only possible for:

• Simple geometry

• Simple Boundary

• Simple Loading.

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. . ACECOMS

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[ The Need for Modeling

A - Real Structure cannot be Analyzed:

It can only be "Load Tested" to determine response

B - We can only analyze a "Model" of the Structure

C - We therefore need tools to Model the Structure and to Analyze the Model

----_^..

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^.

....__^..__..

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^- ^....^{-. -}^{. ..}^--^..•...^- ^{.-.- . -}^..^{- . - -}^...--.---.-.---.-.----~-~..

- - -

Finite Element Method: The Analysis Tool

• Finite Element Analysis (FEA)

- "A discretized solution to a continuum problem using FEM"

• Finite Element Method (FEM)

- "A numerical procedure for solving (partial) differential equations associated with field problems, with an accuracy acceptable to engineers "

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Finite Element Analiysis and Design of RC Buildings - 6

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. . ACECOMS

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[ Continuum to Discrete Model

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Pv ~

3D-CONTINUM CONTINUOUS MODEL DISCRETE MODEL MODEL OF STRUCTURE OF STRUCTURE (Governed by partial (Governed by either (Governed by algebraic differential equations) partial or total differential equations)

equations)

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- _

^..^{_ - -}

[,----~F~m C ' lassical to FEM Solution

.. ------- -- ------....

Classical FEM

Actual Structure Structural Model

- - Kr=R

...

"Partial

Differential

"Algebraic Equations "

Equations"

fo' edY =JP!iICW+ . Jp!iiils

^K⁼^Stiffness

r = Response

(Principle of Virtual Work) ; R = Loads

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Dro Naveed Anwar ~

Asian Institute of Technology, AIT

~

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[ Simplified Structural System

¢

Deformations (D) A

D K

'+--oJ

F -

^{, ,}

F=KD

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- -

^.--^...

_ - - - -

^- ^..

_

^..^..

_ 0_ _ _0"·_··_··_ - ._ __

~~--~---~---~

[ The Structural System

STRUCTURE

¢

^RESPONSES

EXCITATION.

A Pv

• Linear

• Static • Elastic

• Nonlinear

• Dynamic • Inelastic

- - _

^•.._---_^..._-- -_.

Finite Element Analysis and Design of RC Buildings - 8

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Asian Institute of Technology, AIT ~

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[ The Equilibrium Equations

1. Linear-Static Elastic OR Inelastic

Ku=F

2. Linear-Dynamic Elastic

3. Nonlinear - Static Elastic OR Inelastic

4. Nonlinear-Dynamic Elastic OR Inelastic

Mi(t)+CU(t)+Kf{t}+F{t)NL=F(t) ~

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[ Analysis Type

The type of Analysis to be carried out depends on the Structural System

The Type of Excitation (Loads)

- The Type Structure (Material and Geometry) - The Type Response

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[ Some More Solution Types

• Non-linear Analysis

- P-Delta Analysis - Buckling Analysis - Static Pushover Analysis

- Fast Non-Linear Analysis (FNA) Large Displacement Analysis

• Dynamic Analysis

- Free Vibration and Modal Analysis Response Spectrum Analysis Steady State Dynamic Analysis

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[~----~'~-S-t-at-ic-V-S-D-y-n-am--iC---~

• Static Excitation

When tbe Excitation (Load) does not vary rapidly with Time - When the Load can be assumed to be applied "Slowly"

• Dynamic Excitation

- Wben tbe Excitation varies rapidly witb Time - When tbe "Inertial Force" becomes significant

• Most Real Excitation are Dynamic but are considered"Quasi Static"

• Most Dynamic Excitation can be converted to

"Equivalent Static Loads"

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Asian Institute of Technology, AIT ~

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[ Elastic Vs Inelastic

• Elastic Material

Follows the same path during loading and unloading and returns to initial state of deformation, stress, strain etc. after removal of load! excitation

• Inelastic Material

Does not follow the same path during loading and unloading and may not returns to initial state of deformation, stress, strain etc.

after removal of load! excitation

• Most materials exhibit both, elastic and inelastic behavior depending upon level of loading.

Linear Vs Nonlinear

• Linearity

- The response is directly proportional to excitation - (Deflection doubles if load is doubled)

• Non..Linearity

- The response is not directly proportional to excitation - (deflection may become 4 times ifload is doubled)

• Non..linear response may be produced by:

- Geometric Effects' (Geometric non-linearity) Material Effects (Material non-linearity) - Both

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. . ACECOMS

"'

[ Basic Analysis Types

excitation Structure Response

Static Elastic Linear

Static Elastic Nonlinear Static Inelastic Linear Static Inelastic Nonlinear Dynamic Elastic Linear Dynamic Elastic Nonlinear Dynamic Inelastic Linear Dynamic Inelastic Nonlinear

23 ~SJ

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[r----~'Some More Solution Types

• Non-linear Analysis

- P-Delta Analysis - Buckling Analysis - Static Pushover Analysis

- Fast Non-Linear Analysis (FNA) - Large Displacement Analysis

• Dynamic Analysis

- Free Vibration and Modal Analysis - Response Spectrum Analysis - Steady State Dynamic Analysis

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25

Asian Institute of Technology, AfT ~

[ Elastic Vs Inelastic ]

• Elastic Material

- Follows the same path during loading and unloading and returns to initial state of deformation, stress, strain etc. after removal of loadl excitation

• Inelastic Material

- Does not follow the same path during loading and unloading and may not returns to initial state of deformation, stress, strain etc.

after removal of loadl excitation

• Most materials exhibit both, elastic and inelastic behavior depending upon level of loading.

,,---,

[ Linear Vs Nonlinear

• Linearity

- The response is directly proportional to excitation - (Deflection doubles if load is doubled)

• Non-Linearity

- The response is not directly proportional to excitation - (deflection may become 4 times ifload is doubled)

• Non-linear response may be produced by:

- Geometric Effects (Geometric non-linearity) - Material Effects (Material non-linearity) - Both

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Elasticity and Linearity

o

linear, but Inelastic

e o

Elastic.• but nonlinear

e

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[ L~ads to Actions

• Loads

• Load Cases ,

• Load Combinations

• Design Envelopes ,

28 •

Design Actions

Finite Element Analysis and Design of RC Buildings ~ 14

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[ Load Cases

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• Load cases are defined by the user and used for analysis purpose only

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• Static Load Cases

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- DeadLoad

Live Load - Wind Load

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• Earthquake Load Cases

- Response Spectrum Load Cases

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- Time mstory Load Cases

• Static Non-Linear Load Cases

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[ Load Combinations

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I • The Load Combinations may be created by the

program, user defined or a combination of both.

• Some Examples: [Created by the program]

I

^{- 1.4rOL}

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- 1.4rOL + 1.7(LLL + rRLL)

- O.75[1.4rOL + 1.7(LLL +rRLL) + l.7WL]

- O.75[1.4rDL +1.7(LLL + rRLL) ·1.7WL]

- O.9rOL + 1.3WL

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- O.9rOL - 1.3WL

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- 1.1 [1.2rOL +O.5{LLl + rRLl) + 1.0E]

- 1.1 [1.2rOL +O.5{LLl + rRlL) • 1.0E]

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[ Obtaining Envelop Results

Combi Comb2 Comb3 ~ombN

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4oad Case·1

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load Case· 2

I load Case· 3

Envelop Results

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load Case ·M

I II I .'P3.4p.-:_I·>PN

_ {Max,p}

. Totiit]~

^Pi P2 Min,P

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Can Envelop Results be Used for Design?

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• Actions Interact with each other,

P

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effecting the stresses

• For Column Design: P, Mx, My

• For Beam Design: Mx, Vy, l z

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• For Slabs: Mx, My, Mxy

• At least 3 Actions from each combination

must be considered together as set

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• Therefore, Envelop Results Can Not be

Used

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• Every Load Combinations must be used for design with complete "Action Set"

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. . ACECOMS

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[ Design Actions For Static Loads

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• For static loads, ^II

Combinations

Design Actions are

I

obtained as the ..J---+---+--+----1lll ^1/1

cumulative result .A----t---+--+----1 ^u^ra

from each load ^'0

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..J---+---+--+----1g

combination, as set ^..J

for all interacting actions

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• The final or critical

I

Combinations

results from design of all load combinations

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³³ are adopted

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Static, Dynamic and Nonlinear Results

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For a Single Action:

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Static Load Case

Response Spectrum Load Case

I +

^Load

Combination 1 for each Time Step

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Time History Load Case OR 1 for envelop ^Table

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1 for each Load Step

Static Non-linear Load Case OR 1 for Envelop

•

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Dr. Naveed Anwar

~ I '

A · I · sian nstltute 0 f T ^Iec no ogy, h I AIT ACECOMS

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[ Special Load Cases

• Response Spectrum Cases

- All response spectrum cases are assumed to be earthquake load cases

- The output from a response spectrum is all positive.

- Design load combination that includes a response spectrum load case is checked for all possible combinations of signs (+, -) on the response spectrum values

- A 3D element will have eight possible combinations of P, M2 and M3 and eight combinations for M3, V, T

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Response Spectrum Results for Action Set

Design Actions needed for Columns:

+P, +Mx, +My +P,+Mx,-My +P, -Mx, +My

Maximum Results obtained by: +P, -Mx,-My

SRSS, CQC, etc.

' f - - - t

. . . -P, +Mx, +My

...

P,Mx,My> -P, +Mx, -My -P, -Mx, +My -P, -Mx, -My I

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Fini,te Element Analysis and Design of RC Buildings - 18

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Dr. Naveed Anwar

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. . ACECOMS

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I L '---~~ -- me-H-is-to-ry-A-n-al-YS-iS-Re-s-u-lt-s

- - - - 0

option - 2:

Design For All Values

I • (At each time step)

I

^{, -} ^{. .}

.

...~~i\;.o~)

t

Lt:'~L...wjl~~~j~-.lIt...i...;~~

~1 •• ,.ll'.rnl.~I'.n ln

I .at.J.I'J•• rll'rJ•• ~ •• 1

7."II7""f'!r-~~~~r~""~r)""r.!l~f!'!'p::!~

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Response Curve for One Action

I I

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I

- - _._ -- -

I

Max Val

Option -1:

Envelope Design

Min Val

~~---~

[ Time History Results

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• The default design load combinations do not include any time history results

Define the load combination, to include time history forces in a design load combination

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• Can perform design for each step of Time

History or design for envelops for those resultsr-;;:;;;;;:;;;=;::;;:;;:;;;;:;;;:;;::;;;:;;;;;;;;

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• For envelope design, the design is for the

maximum of each response quantity (axial load, moment, etc.) as if they occurred simultaneously.

• Designing for each step of a time history gives correct correspondence between different response quantities

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. . ACECOMS

ASian Institute of Technology

^I

AIT

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"--~---,

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[ Time History Results

- ...:. The program gets a maximum and a minimum value for each

I

response quantity from the envelope results for a time history

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- For a design load combination any load combination that includes a time history load case in it is checked for all possible combinations of maximum and minimum time history design

values.

I

- If a single design load combination has more than one time history case in it, that design load combination is designed for

I

the envelopes of the time histories, regardless of what is

specified for the Time History Design item in the preferences

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[~--~" Static Non Linear Results I

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- The default design load combinations do not include any Static Nonlinear results

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- Define the load combination, to include Static Nonlinear

Results in a design load combination

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For a single static nonlinear load case the design is

performed for each step of the static nonlinear analysis.

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Wind load Cases

At least 3 basic Wind Load Cases should be considered

- Along X-Direction

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- Along Y Direction

- Along Diagonal

• Each Basic Wind Load Case should

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be entered separately into load

combinations twice, once with (+ve) and once with (-ve) sign

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• Total of 6 Wind Load Cases should

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considered in Combinations, but only 3 Load Cases need to be defined and analyzed

Wx~

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I I['---~' Wind load Combinations

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(t) Is the load factor specified for Example:

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Wind in the design codes Comb = O.75(1.4D + 1.7W) will

need Six Actua]' Combinations Six Additional Load Combinations

Combl= O.75(1.4D + 1.7Wx) are required where ever "Wind" is

Comb2 = O.75(1.4D - 1.7Wx)

I

mentioned in the basic Load! Comb3 = O.75(1.4D + 1.7Wy)

Combinations

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Comb4 = O.75(1.4D - 1.7Wy) Comb5 = O.75(1.4D + 1.7Wxy) Comb6 = O.75(1.4D - 1.7Wxy)

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Dr. Naveed Anwar

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Asian · I ·nstltute 0f TechnoIogy, AIT ^ACECOMS

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[ T he Building Structural System

• The Gravity Load Resisting System (GLRS) I

- The structural system (beams, slab, girders, columns, etc)

that act primarily to support the gravity or vertical loads

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• The 'lateral Load Resisting System (LLRS)

- The structural system (columns, shear walls, bracing, etc) that primarily acts to resist the lateral loads

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• The Floor Diaphragm (FD)

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- The structural system that transfers lateral loads to the lateral load resisting system and provides in-plane floor

stiffness

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Asian Institute of Technology, AIT ~

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[ Main Slab Types: Usage

I • Buildings

- Flat Slabs, One way Slabs, Two way Slabs

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- Isolated Footings, Combined Footings, Rafts

- Pre-cast slab panels, hollow core slabs

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• Bridges and Highways

Deck Slab on Girders - Box Girder Slabs

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- Slab on Grade: Pavements, Approach Slabs,

• Water Retaining Structures

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- Retaining Wall Systems

- Tank Roof and Floor slabs

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[ Basic Definition

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• Plate

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- Any member, or part of member whose thickness is much

less than its other dimensions

• Slab

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- A plate resting on supports, generally horizontal and transferring vertical loads directly.

I • Slab System

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A combination of various components, such as slabs, beams, drop panels, stiffeners, joists, girders, ribs, all acting

together to transfer the loads to supports

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