System Design Fundamentals January 2011

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System Design FundamentalsJanuary 2011

• Dr. Abdul Razzaq Touqan

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System Design Fundamentals
Objectives -to introduce the building
construction determinant -to analyze different
systems by finite element method and analogical
methods -to build conceptual abilities in
designing reinforced concrete elements.
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Preface

• Most of the education and research is
  concentrated in analytical skills and very little
  in creativity skills (analogical skills) which is
  fundamental in design.
• Creativity is the ability to conceive, generate
  design alternatives and preserve environment. It
  requires compositional ability.
• Compositional ability requires conceptual
  understanding which is based on both a feeling
  for behavior and approximate analysis\design
  skills

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Preface

• System design addresses the need for conceptual
  design skills.
• A design project provides opportunity for teams
  of students to create conceptual designs and make
  representations to a design jury.
• It provides opportunity to concentrate on the
  structure as a whole and very little on the
  element behaviour.

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Chapter 1 Introduction

• Introduction to systems
• Purpose
• System determinants
• Example 1
• Standards versus codes
• Problem set 1 (due )
• Fundamentals of thinking

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Introduction to systems

• A system is a necessary part of life. It occurs
  at any level, ranging from the molecular
  structure of material to laws of universe.
• As order, it relates all the parts of a whole
  reflecting some pattern of organization.
• Everything has system, even if we have not yet
  recognized it. Societies are a form of structural
  systems to properly function- language has
  system, the interrelationship of plants and
  animals with their environment represents
  equilibrium in nature which is a system by
  itself.

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Purpose

• The purpose of a system is to combine global
  understanding with local details.
• Discuss face of human being and how
  systematically it combines architectural,
  structural, mechanical and electrical systems

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System determinants

• Engineering systems must develop
• Support system (structure\science)
• It holds the structure up so that it does not
  collapse. A need for strength to achieve this.
• It prevents elements to deform or crack
  excessively. A need for serviceability to achieve
  this.
• It makes the structure withstands severe events
  (like earthquakes, wind storms, ). A special
  design is needed to achieve this (savings in
  materials smaller sections larger strength).

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System determinants

• Faith system (facts/fashion)
• It Defines
• space configuration based on functional needs
  (social, economical),
• The capacity of adaptation based on freedom needs
  (legal, environmental)
• geometrical shape based on form needs (culture,
  esthetics)

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Example 1

• A client likes to build a carage for his car. If
  the car dimensions are 5mX2mX1.5m height. Select
  a value for the dimensions shown and defend your
  selection in no more than 20 words (note a
  family of acceptable design solutions can be done
  as long as they achieve system determinants)

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Example 1 continues
Reasoning Selected Dimension in meter Proposed Dimensions in meter
a4.5, 5.5, 6.5
b2.3, 2.7, 3.1
t0.1, 0.2, 0.3
h1.8, 2.5, 3.5
d0.15, 0.30, 0.5
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Standards versus codes

• Minimum standards are controlled by design
  (ethic) codes.
• Design codes are based on model codes which often
  specify a particular industry standard.
• Municipal and state governments adopt the model
  codes (or develop their own codes) and thus
  provide legally enforceable laws with which the
  engineer must comply.
• The intent of the code is not to limit
  engineering creativity, but to provide minimum
  standards to safeguard the health and safety of
  the public.

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Problem set 1 (Project due )

• Plan of a land and permitted building area is
  shown next with municipality main water line and
  manhole for waste water disposal. The allowable
  bearing capacity of the soil is 0.4MPa
• The design determinants for a preliminary study
  are

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General layout plan
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Problem set 1 continued

• Prepare a draft first floor plan for parking.
• Prepare a draft plan to serve two residential
  apartments in each floor (3.12m elevation) and
  specify number of stories allowed according to
  your local code.
• Prepare a draft mechanical and electrical plan
  for first floor and show on it connections from
  the building to municipality lines.
• Defend your ideas in no more than 150 words and
  in points.
• You must work in groups of 5 each, each group
  must select one choice of a and b as provided
  next page with the help of the instructor.

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Fundamentals of thinking Input

• Start with present worked examples (get advantage
  of other thoughts-how Japan builds up quickly).
• See (a good engineer is a good observer),
• Read (plans of others),
• Ask (learn how to gather hidden information
  making sure you are satisfied with the answer, if
  not then argue but be careful not to go more than
  one round for each point (learn how to express
  yourself in words))

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Fundamentals of thinking Input and Processing

• Try to solve the problem by
• Study your subject first of all.
• Get an overview about all tasks needed for
  solution.
• Select members of your team based on
  qualifications capability to do the work
  commitment.
• Choose a qualified team leader.
• Divide the tasks between the team members.
• Put a study plan (allocate time for each task
  plan alternatives).
• Think how to do your part of the work on paper
  (learn how to express yourself in writing).

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Fundamentals of thinking Processing and Output

• Systematical management of tasks
• Survey literature of the subject (system
  determinants). Be careful to cover all sides of
  the problem.
• Put a plan how to cover general principles before
  particular ones
• Make sure to stress the important issues and
  basic principles (support your work by scientific
  proof)
• Put contents of your final report
• Unify with your team members all symbols,
  wording, software etc to be used to present the
  final report.
• Perform your study plan and see how well it is.
• Get feed back from all your team members about
  the whole project to decide to continue or go to
  alternatives

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Chapter 2 Design methodology

• Limit States Design
• Strength Limit State
• Serviceability Limit State
• Special Limit State
• Limit States Design
• Design Philosophy
• Strength Design Method
• Safety Provisions
• Variability in Resistance
• Variability in Loading
• Consequences of Failure
• Margin of Safety

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Limit State Design

• Limit State
• Condition in which a structure or structural
  element is no longer acceptable for its intended
  use.
• Major groups for RC structural limit states
• Strength
• Serviceability
• Special

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Strength Limit State

• Structural collapse of all or part of the
  structure ( very low probability of occurrence)
  and loss of life can occur (a structure will not
  fail as long as there is a safe load path to the
  foundation). Major limit states are
• (a) Loss of equilibrium of a part or all of a
  structure as a rigid body (tipping, sliding of
  structure reaction could not be developed).
• (b) Rupture of critical components causing
  partial or complete collapse. (flexural, shear
  failure).

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Strength Limit States

• (c) Progressive Collapse
• Minor local failure overloads causing adjacent
  members to fail until entire structure collapses.
• Structural integrity is provided by tying the
  structure together with correct detailing of
  reinforcement which provides alternative load
  paths to prevent localized failure.

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Serviceability Limit State

• Functional use of structure is disrupted, but
  collapse is not expected. More often tolerated
  than a strength limit state since less danger of
  loss of life. Major limit states are
• (a) Excessive crack width leads to leakage which
  causes corrosion of reinforcement resulting in
  gradual deterioration of structure.
• (b) Excessive deflections for normal service
• malfunction of machinery
• visually unacceptable
• damage of nonstructural elements
• changes in force distributions (no compatibility)
• ponding on roofs leading to collapse of roof

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Serviceability Limit State

• (c ) Undesirable vibrations
• Vertical floors/ bridges
• Lateral\torsional tall buildings

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Special Limit State

• Damage/failure caused by abnormal conditions or
  loading. These could be due to
• (a) Extreme earthquakes damage/collapse
• (b) Floods damage/collapse
• (c) Effects of fire, explosions, or vehicular
  collisions.
• (d) Effects of corrosion, deterioration
• (e) Long-term physical or chemical instability

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Limit States Design

• Identify all potential modes of failure.
• Determine acceptable safety levels for normal
  structures building codes load combination
  factors.

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Limit States Design

• Consider the significant limit states.
• Members are designed for strength limit states
• Serviceability is checked.
• Exceptions may include
• water tanks (crack width)
• monorails (deflection)
• Noise in auditoriums

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Design Philosophy
Two philosophies of design have long
prevalent. (a)Working stress method focusing on
conditions at service loads. (b)Strength design
method focusing on conditions at loads greater
than the service loads when failure may be
imminent. The strength design method is deemed
conceptually more realistic to establish
structural safety.
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Strength Design Method
In the strength method, the service loads are
increased sufficiently by factors to obtain the
load at which failure is considered to be
imminent. This load is called the factored
load or factored service load.
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Strength Design Method
Strength provided is computed in accordance with
rules and assumptions of behavior prescribed by
the building code and the strength required is
obtained by performing a structural analysis
using factored loads. The strength provided has
commonly referred to (wrongly) as ultimate
strength. However, it is a code defined value
for strength and not necessarily ultimate. The
ACI Code uses a conservative definition of
strength.
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Safety Provisions
Structures and structural members must always be
designed to carry some reserve load above what is
expected under normal use.
There are three main reasons why some sort of
safety factor are necessary in structural
design. 1 Variability in resistance. 2
Variability in loading. 3 Consequences of
failure.
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Variability in Resistance R

• Variability of the strengths of concrete and
  reinforcement.
• Differences between the as-built dimensions and
  those found in structural drawings.
• Effects of simplification made in the derivation
  of the members resistance (i.e. simplifying
  assumptions).

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Variability in Resistance R
Comparison of measured and computed failure
moments based on all data for reinforced concrete
beams with fc gt 14MPa The variability shown is
due largely to simplifying assumptions.
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Variability in sustained Loads S
Frequency distribution of sustained component of
live loads in offices. In small
areas Average0.65kN/m2 1 exceeded2.2kN/m2 Cod
e use 2.5kN/m2 In large areas average almost
the same, but variability decreases. (notice
that large areas can be used for parties,
temporary storageetc, thus larger LL is
needed)
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Consequences of Failure
A number of subjective factors must be considered
in determining an acceptable level of safety.

• Potential loss of life larger SF for auditorium
  than a storage building.
• Cost of clearing the debris and replacement of
  the structure and its contents.
• Cost to society collapse of a major road.
• Type of failure, warning of failure, existence of
  alternative load paths.

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Margin of Safety
The term Y R - S is called the safety margin.
The probability of failure is defined as and
the safety index is
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Problem set 2 Due ( )

• Types of design can be classified as
• Creative
• Development
• Copy
• Analyze previous types showing advantages and
  disadvantages of each type in view of what you
  learned from previous two chapters.

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Chapter 3 Loadings

• Loading Specifications
• Dead Loads
• Live Loads
• Environmental Loads
• Classification of Buildings for Wind, Snow and
  Earthquake Loads
• Snow Loads
• Earthquake Loads
• Roof Loads
• Construction Loads
• Load factors

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Building Codes

• Cities in the U.S. generally base their building
  code on one of the three model codes
• Uniform Building Code
• Basic Building Code (BOCA)
• Standard Building Code

These codes have been consolidated in the 2000
International Building Code.
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Loading Specifications
Loadings in these codes are mainly based on
ASCE Minimum Design Loads for Buildings and Other
Structures ASCE 7-05.
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Dead Loads

• Weight of all permanent construction
• Constant magnitude and fixed location
• Examples
• Weight of the Structure
• (Walls, Floors, Roofs, Ceilings, Stairways)
• Fixed Service Equipment
• (HVAC, Piping Weights, Cable Tray, etc.

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Live Loads

• Loads produced by use and occupancy of the
  structure.
• Maximum loads likely to be produced by the
  intended use.
• Not less than the minimum uniformly distributed
  load given by Code.

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Live Loads
See Table 4-1 from ASCE 7-05 Stairs and
exitways 4.8KN/m2. Storage
warehouses 6KN/m2 (light) 12 KN/m2
(heavy) Minimum concentrated loads are also
given in the codes.
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Live Loads
ASCE 7-05 allows reduced live loads for members
with influence area (KLL AT) of 38m2 or more (not
applied for roof) where L ? 0.50 Lo for
members supporting one
floor ? 0.40 Lo otherwise KLL live load
element factor (Table 4.2) 2 for beams 4
for columns
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Environmental Loads

• Snow Loads
• Earthquake
• Wind
• Soil Pressure
• Roof Loads
• Temperature Differentials
• etc

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Classification of Buildings for Wind, Snow and
Earthquake Loads
Based on Use Categories (I through IV)
Buildings and other structures that represent a
low hazard to human life in the event of a
failure (such as agricultural facilities),
I1 Buildings/structures not in categories I,
III, and IV, I1
I II
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Classification of Buildings for Wind, Snow and
Earthquake Loads
Buildings/structures that represent a substantial
hazard to human life in the event of a failure
(assembly halls, schools, colleges, jails,
buildings containing toxic/explosive substances),
I1.25
III
Buildings/structures designated essential
facilities (hospitals, fire and police stations,
communication centers, power-generating
stations), I1.5
IV
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Snow Loads

• Ground Snow Loads
• Based on historical data (not always the maximum
  values)
• Basic equation in codes is for flat roof snow
  loads
• Additional equations for drifting effects, sloped
  roofs, etc.
• Use ACI live load factor
• No LL reduction factor allowed
• Use 1KN/m2 as minimum snow load, multiply it by I
  (importance factor)

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Earthquake Loads

• Inertia forces caused by earthquake motion
• F m a
• Distribution of forces can be found using
  equivalent static force procedure (code, not
  allowed for every building) or using dynamic
  analysis procedures (computer applications).

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Roof Loads

• Ponding of rainwater
• Roof must be able to support all rainwater that
  could accumulate in an area if primary drains
  were blocked.
• Ponding Failure (steel structures)
• ? Rain water ponds in area of maximum
  deflection
• ? increases deflection
• ? allows more accumulation of water ? cycle
  continues? potential failure
• Roof loads (like storage tanks) in addition to
  snow loads
• Minimum loads for workers and construction
  materials during erection and repair

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Construction Loads

• Construction materials
• Weight of formwork supporting weight of fresh
  concrete
• Basement walls
• Water tanks

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Load factors
The loading variations are taken into
consideration by using a series of load factors
to determine the ultimate load, U.
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Load factors
The equations come from ACI code 9.2 D Dead
Load L Live Load E Earthquake Load W Wind
Load
The most general equation for the ultimate load,
U (Mu) that you will see is going to be
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Problem set 3

• Ribbed slab construction is common in Palestine.
  Construct an allowable load table and an ultimate
  load table for common sizes of rib-construction.
  The table should include block (density 12KN/m3 )
  and eitong (density 5.5KN/m3 ) of different sizes
  against different values of superimposed loads (1
  to 4KN/m2 in 0.5 increments).

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Element design

• 4.1 Short Columns
• 4.2 Beams
• 4.2.1 Flexure
• 4.2.2 Serviceability
• 4.2.3 Shear
• 4.2.4 Bar development
• 4.2.5 Bar splices in tension
• 4.3 Footings

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4.1 Short Columns
General Information
Vertical Structural members Transmits axial
compressive loads with or without moment transmit
loads from the floor roof to the foundation
Columns
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Short Columns revision
General Information

• Column Types
• Tied
• Spiral
• Composite
• Combination
• Steel pipe

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Short Columns revision
Tied Columns - 95 of all columns in
buildings in nonseismic regions are tied
Tie spacing b (except for seismic) tie
supports long bars (reduces buckling) ties
provide negligible restraint to lateral expose of
core
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Short Columns revision
Spiral Columns
Pitch 2.5cm to 7.5cm spiral restrains lateral
(Poissons effect) axial load delays failure
(ductile)
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Short Columns revision
Behavior
An allowable stress design procedure using an
elastic analysis was found to be unacceptable.
Reinforced concrete columns have been designed by
a strength method since the 1940s.
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Short Columns revision
Initial Behavior up to Nominal Load - Tied and
spiral columns.
1.
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Short Columns revision
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Approximate Analysis

• Use of tributary area area of floor or roof
  which supports all of the loads whose load path
  leads to the column.
• Use load path slab reactions carried by beams.
  Beam reactions carried by columns.

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Design of Short Columns
Let Ag Gross Area bh
Ast area of long steel
fc concrete compressive strength
fy steel yield strength
Factor due to less than ideal consolidation and
curing conditions for column as compared to a
cylinder. It is not related to Whitneys stress
block.
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Design of Short Columns
Maximum Nominal Capacity for Design Pn (max)

2.
ACI 10.3.6.1-2
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Design of Short Columns
Reinforcement Requirements (Longitudinal Steel
Ast)
3.
Let
- ACI Code requires
-ACI 10.8.4 use half Ag if column section is much
larger than loads.
-Minimum of Bars (ACI Code 10.9.2) 6 in
circular arrangement and 4 in rectangular
arrangement
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Design of Short Columns
3.
Reinforcement Requirements (Lateral Ties)
Vertical spacing (ACI 7.10.5.1-3)
10mm bars least dimension of tie
Every corner and alternate longitudinal bar shall
have lateral support provided by the corner of a
tie with an included angle not more than 135o,
and no bar shall be more than 15cm clear on
either side from support bar.
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Design of Short Columns
Examples of lateral ties.
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Design of Short Columns
3. Reinforcement Requirements (Spirals )
ACI Code 7.10.4
size
10mm dia.
clear spacing between spirals
2.5cm
7.5cm
ACI 7.10.4.3
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Design of Short Columns
4.
Design for Concentric Axial Loads
(a) General Strength Requirement

• 0.65 for tied columns
• 0.75 for spiral columns (ACI 08)

where,
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Design of Short Columns
4.
Design for Concentric Axial Loads
(b) Expression for Design
defined
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Design of Tied Short Columns

• The ultimate load is found using tributary area
• and number of stories
• The design load can be approximated as follows

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Approximate Design of Short Columns

• For a tied column with 1 steel reinforcement

For 20MPa concrete strength and 420MPa yield
strength and representing gross area in cm2 and
column capacity in kN
Thus the area of column in square cm represents
approximately its capacity in kN
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Length to width ratio

• Condition for short columns braced
• Thus if the height to width ratio is less than 15
  (the mean value) the column is classified as short

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Problem set 4

• Common practice is to build four stories with 4m
  span dimensions. What is the size of the column
  needed to support a common 25cm rib construction
  (17cm height blocks, 15cm ribs).
• Common practice in the last 50years is to use
  614mm bars in columns 25cmX50cm, thus a use of
  0.72 instead of 1 minimum. Comment!
• In the nineties trying to build columns with 2
  reinforcement using common technology at that
  time yields to honeycombing, comment!
• Is it wise to design columns according to minimum
  design requirements, comment!

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Beams4.2.1 Flexure
The beam is a structural member used to support
the internal moments and shears. It would be
called a beam-column if a compressive force
existed. C T M C(jd)
T(jd)
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Flexure
The first beam fails in shear, the second fails
in bending moment.
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Approximate analysis

• Use of tributary area (area of floor or roof
  which supports all of the loads whose load path
  leads to the beam) determines the beam load.
• Perform approximate analysis through
• Approximate deflected shape to locate points of
  inflection, hence transform to determinate beam
  and analyze using statics.
• Use analysis coefficients (e.g. ACI coefficients)
• Use finite element programs

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Design for Flexure review
Basic Assumptions in Flexure Theory

• Plane sections remain plane ( not true for deep
  beams h gt 4b)
• The strain in the reinforcement is equal to the
  strain in the concrete at the same level, i.e. es
  ec .
• Stress in concrete reinforcement may be
  calculated from the strains using f-e curves for
  concrete steel.
• Tensile strength of concrete is neglected.
• Concrete is assumed to fail in compression, when
  ec 0.003
• Compressive f-e relationship for concrete may be
  assumed to be any shape that results in an
  acceptable prediction of strength.

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Design for Flexure review
The compressive zone is modeled with an
equivalent stress block.
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Design for Flexure review
Example of rectangular reinforced concrete beam.
Setup equilibrium.
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Design for Flexure review
The ultimate load, which is used in the design
and analysis of the structural member is Mu
Ultimate Moment Mn Nominal Moment ?
Strength Reduction Factor The strength reduction
factor, ?, varies depending on the tensile strain
in steel in tension. Three possibilities
Compression Failure - (over-reinforced
beam) Tension Failure - (under-reinforced
beam) Balanced Failure - (balanced reinforcement)
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Design for Flexure review
Which type of failure is the most desirable?
The under-reinforced beam is the most
desirable. fs fy es gtgt ey You want ductility
system deflects and still carries load.
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Approximate Design for Flexure J
For under-reinforced, the equation can be
rewritten as
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Approximate Design for Flexure J
rmax maximum r value recommended to get
simultaneous ec 0.003 es 0.005
Use similar triangles
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Approximate Design for Flexure J
For a yield stress 420MPa, the equation can be
rewritten to find c as
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Approximate Design for Flexure J
The strength reduction factor, f, will come into
the calculation of the strength of the beam.
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The factor J for large steel ratios

• For concrete strength variation 20MPa to 42Mpa,
  the value of J for maximum recommended steel
  ratio varies is 0.317. Moment in kN.m, area of
  steel in square cm and depth in cm.

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Limitations on Reinforcement Ratio, r
Lower Limit on r ACI 10.5.1

ACI Eqn. (10-3) fc fy are in MPa Lower
limit used to avoid Piano Wire beams. Very
small As ( Mn lt Mcr ) Strain in steel is huge
(large deflections) when beam cracks (Mu/?gt Mcr )
beam fails right away because nominal capacity
decreases drastically.
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The factor J for minimum steel ratios

• For concrete strength variation 20MPa to 42Mpa,
  the value of J for minimum steel varies from 0.36
  to 0.37

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The factor J

• It is obvious that variation of J is not
  sensitive to changes in concrete strength. Thus a
  mean value of 0.33 is representative for all
  types of concrete used in Palestine (B250-B500)

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Additional Requirements for Lower Limit on r
Temperature Shrinkage reinforcement in
structural slabs and footings (ACI 7.12) place
perpendicular to direction of flexural
reinforcement. GR 40 or GR 50 Bars As (TS)
0.0020 Ag GR 60 As (TS) 0.0018 Ag Ag -
Gross area of the concrete
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4.2.2 Beams serviceability

• Beam Depths
• ACI 318 - Table 9.5(a) min. h based on span
  (slab beams)
• Design for max. moment over a support to set
  depth of a continuous beam.

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4.2.3 Shear
Typical Crack Patterns for a deep beam.
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Shear Design review
Shear Strength (ACI 318 Sec 11.1)
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Shear Design review\ Minimum Shear Reinforcement
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Approximate design for shear

• Better to use
• Hence

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Shear Design review/ max shear
Compression fan carries load directly into
support.
Non-pre-stressed members
Sections located less than a distance d from face
of support may be designed for same shear, Vu, as
the computed at a distance d.
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Shear Design review/ max shear
When
1. The support reaction introduces compression
into the end regions of the member. 2. The loads
are applied at or near the top of the beam. 3. No
concentrated load occurs with in d from face of
support .
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Shear Design review/ max shear
Compression from support at bottom of beam tends
to close crack at support
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4.2.4 Development Length
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4.2.5 Bar Splices in tension
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Types of Splices
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Types of Splices
Class B Splice
(ACI 12.15.2)
All tension lab splices not meeting requirements
of Class A Splices
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Tension Lap Splice (ACI 12.15)
where As (reqd) determined for bending ld
development length for bars (not allowed
to use excess reinforcement modification
factor) ld must be greater than or
equal to 30cm Lab Splices should be placed in
away from regions of high tensile stresses
-locate near points of inflection (ACI R12.15.2)

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4.3 Footings
Definition
Footings are structural members used to support
columns and walls and to transmit and distribute
their loads to the soil in such a way that the
load bearing capacity of the soil is not
exceeded, excessive settlement, differential
settlement,or rotation are prevented and
adequate safety against overturning or sliding is
maintained.
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Types of Footings
Wall footings are used to support structural
walls that carry loads for other floors or to
support nonstructural walls.
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Types of Footings
Isolated or single footings are used to support
single columns. This is one of the most
economical types of footings and is used when
columns are spaced at relatively long distances.
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Types of Footings
Combined footings usually support two columns,
or three columns not in a row. Combined footings
are used when two columns are so close that
single footings cannot be used or when one column
is located at or near a property line.
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Types of Footings
Cantilever or strap footings consist of two
single footings connected with a beam or a strap
and support two single columns. This type
replaces a combined footing and is more
economical.
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Types of Footings
Continuous footings support a row of three or
more columns. They have limited width and
continue under all columns.
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Types of Footings
Rafted or mat foundation consists of one footing
usually placed under the entire building area.
They are used, when soil bearing capacity is low,
column loads are heavy, single footings cannot be
used, piles are not used and differential
settlement must be reduced.
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Types of Footings
Pile caps are thick slabs used to tie a group of
piles together to support and transmit column
loads to the piles.
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Distribution of Soil Pressure
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Design Considerations
Footings must be designed to carry the column
loads and transmit them to the soil safely while
satisfying code limitations.
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Size of Footings
The area of footing can be determined from the
actual external loads such that the allowable
soil pressure is not exceeded.
Strength design requirements
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Two-Way Shear (Punching Shear)
For two-way shear in slabs ( footings) Vc is
smallest of
ACI 11-31
When gt 2 the allowable Vc is reduced.
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Design of two-way shear
Assume d. Determine b0. b0 4(cd) b0
2(c1d) 2(c2d)
1. 2.
127
Design of two-way shear
The shear force Vu acts at a section that has a
length b0 4(cd) or 2(c1d)
2(c2d) and a depth d the section is subjected
to a vertical downward load Pu and vertical
upward pressure qu.
3.
128
Design of two-way shear
Allowable Let VufVc
4.
If d is not close to the assumed d, revise your
assumptions
129
Design of one-way shear
For footings with bending action in one direction
the critical section is located a distance d from
face of column
130
Design of one-way shear
The ultimate shearing force at section m-m can be
calculated
131
Design of one-way shear
If no shear reinforcement is to be used, then d
can be checked, assuming Vu fVc

132
Approximate Flexural Strength and Footing
reinforcement
The bending moment in each direction of the
footing must be checked and the appropriate
reinforcement must be provided.

133
Flexural Strength and Footing reinforcement
The minimum steel percentage required shall be as
required for shrinkage temperature reinforcement.

134
Problem set 5

• Design a panel 4m by 5m supported on four
  columns.
• Design the slab as one-way rib in the 4m
  direction. The superimposed load is 3kN/m2, the
  live load is 3kN/m2
• Design the beam, column and isolated footing to
  support four stories, concrete is B250 .
• Soil allowable bearing capacity is 350kN/m2

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System analysis and design

• 5.1. Regular systems
• 5.2. Ribbed slab systems
• 5.3. Two way slab systems
• If time permits
• 5.4. Systems without vertical continuity
• 5.5. General shape building systems

137
5.1 Regular systems

• Regular systems are those which have one way
  solid slab and vertical continuity i.e. load of
  slab is transferred to beams, from beams to
  columns and then to footings.
• Analysis of all systems are done using either 1D,
  2D or 3D modeling.

138
Regular systems example

• 1-storey RC slab-beam factory structure shown
  next slide
• Fixed foundations, 4 spans 5m bays in x and a
  single 8m span in y, 6m elevation
• E24GPa, µ0.2, ?2.5t/m3
• Cylinder concrete strength25MPa, steel
  yield420MPa
• superimposed loads5kN/m2, live load9kN/m2

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Regular systems example

• Due to cracking of elements, use the following
  modifiers for gross inertia for 3D analysis (ACI
  R10.11.1)
• Beam 0.35
• Column 0.7
• One way slab (0.35, 0.035)

141
Preliminary dimensioning

• Slab According to ACI 9.5.2 thickness of
  slab500/2420.83cm, but considering that
  concentrated loads might be placed at middle of
  slab, use 25cm thickness
• Beam 800/1650cm, however beams fail by strength
  and not deflection, and because it is a factory
  use drop beams 30cmX80cm (6cm cover)
• Columns use 30X60cm reinforced on two faces
  (cover 4cm).

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1D analysis and design slab model

143
1D analysis and design slab analysis
144
1D analysis and design slab analysis

• wd(.2524.55)11.125KN/m
• wl9KN/m
• wu1.211.1251.6927.75KN/m

145
1D analysis and design slab analysis, BM in
KN.m, As in square cm
146
1D analysis and design slab analysis, values of
reactions in KN

• Note for slabs and footings of uniform thickness
  the minimum steel is that for temperature and
  shrinkage but with maximum spacing three times
  the thickness or 450mm. (ACI10.5.4)

147
1D analysis and design beam analysis,

• Assume simply supported beam
• Beam C, Mu(1291.20.3.824.5)82 /81088
• Beam B, Mu(1591.20.3.824.5)82 /81328
• Beam A, Mu(54.51.20.3.824.5)82 /8492

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3D SAP Gravity equilibrium checks

• D
• Slab20X8X(0.25X24.55)1780KN
• Beams(5X82X20)X.8X.3X24.5470KN
• Columns10X6X.3X.6X24.5264.6KN
• Sum2514.6KN
• L
• R 20X8X91440KN

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Gravity equilibrium checks

• SAP results

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BM in beams in interior frame (KN.m)
152
Design for D and L (1.2D1.6L)

• Conceptual check for dead
• Wd(.25X24.55)X555.6KN/m
• Md55.6X82 /8445KN.m (compare with
  250190440KN.m ok)
• Conceptual check for live
• WL9X545KN/m
• ML45X82 /8360KN.m (compare with 182136318KN.m
  ok)
• Conceptual design for positive moment
• Mu1.22501.6182591KN.m
• As3591/7424cm2.

153
Reinforcement calculation
154
Conclusion

• If 3D analysis results are used conceptual
  understanding of edge beam is wrong, thus expect
  failure in torsion

155
Problem set 6

• Analyze and design a one story reinforced
  concrete structure (entertainment hall) made of
  one way solid slab sitting on drop beams
  supported on six square columns 50cm dimensions.
  The superimposed and live loads are 3KN/m2 and
  4KN/m2 respectively.

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5.2 Ribbed slab systems
View of Pan Joist Slab from Below
159
Pan Joist Floor Systems

• Definition The type of slab is also called a
  ribbed slab. It consists of a floor slab,
  usually 5-10cm thick, supported by reinforced
  concrete ribs. The ribs are usually uniformly
  spaced at distances that do not exceed 75cm. The
  space between ribs is usually filled with
  permanent fillers to provide a horizontal slab
  soffit.

160
Pan Joist Floor Systems

• ACI Requirements for Joist Construction
• (Sec. 8.13, ACI 318-08)
• Slabs and ribs must be cast monolithically.
• Ribs may not be less than 10cm in width
• Depth of ribs may not be more than 3.5 times the
  minimum rib width
• Clear spacing between ribs shall not exceed 750mm
• Ribbed slabs not meeting these requirements
  are designed as slabs and beams.

161
Pan Joist Floor Systems

• Slab Thickness
• (ACI Sec. 8.13.6.1)
• t 5cm
• t one twelfth the clear distance between
  ribs

Building codes give minimum fire resistance
rating 1-hour fire rating 2cm cover, 7.5-9cm
slab thick. 2-hour fire rating 2.5cm cover,
12cm slab thick. Shear strength
162
Pan Joist Floor Systems

• Laying Out Pan Joist Floors (cont.)
• Typically no stirrups are used in joists
• Reducing Forming Costs
• Use constant joist depth for entire floor
• Use same depth for joists and beams (not always
  possible)

163
Pan Joist Floor Systems

• Distribution Ribs
• Placed perpendicular to joists
• Spans lt 6m. None
• Spans 6-9m Provided at midspan
• Spans gt 9m Provided at third-points
• At least one continuous 12mm bar is provided at
  top and bottom of distribution rib.
• Note not required directly by ACI Code, but
  typically used in construction and required
• indirectly in ACI 10.4.1

164
Ribbed Slab example

• Analyze and design (as a one-way ribbed slab in
  the 7m direction) the following one story
  structure (3m height) using 3D model (figure next
  slide)
• A. Specifications B250, fy4200 kg/cm2,
  superimposed 70 kg/m2 , live loads 200 kg/m2,
  ribs 34cm height/ 15cm width, blocks 40X25X24cm
  height (density1t/m3 ), beam 25cm width by 50cm
  depth, column dimensions 25cmX25cm,

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Local practice slab-beam-column construction

• Slab assume c5cm
• wd(0.15.240.550.1)2.50.40.241/0.550.07
  0.658t/m2
• wu 1.20.6581.60.20.550.61t/m/rib
• Mu- 0.61(2.5)2 /21.91t.m., As1.87cm2.
• Mu 2.84t.m., As2.64cm2
• verify that change of shape (rectangular) or fc
  (take 300) has minor effect on change of As

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Beam analysis and design

• Beam B1 (interior frame)
• wu (3.93/0.55)0.250.52.51.2 7.52 t/m
• Mu- 7.52(6)2 /833.8t.m., As33.8X30/4522.6cm2
• Mu 7.52(6)2 /14.219.1t.m., As19.1X30/4512.7cm
  2
• Beam B2 (exterior frame)
• wu (1.86/0.55)0.250.52.51.2 3.76 t/m
• Mu- 3.76(6)2 /816.9t.m., As16.9X30/4511.3cm2
• Mu 3.76(6)2 /14.29.53t.m., As9.53X30/456.4cm2
  

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3D Model
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Problem set 7

• Repeat previous example but if the beams are 34cm
  depth by 37cm width .(to preserve beam weight)
• Draw conclusions

173
Problem set 7 (solution)
174
Problem set 7 (solution)

• Conclusions Ribs
• Moments increased on interior column strip and
  reduced on interior middle strip, which increases
  the difference existed previously. Why?
• Do you expect problems in local practice, why?
  Yes, at cantilevers due to large increase

175
Problem set 7 (solution)

• Conclusions beams
• All moments are reduced (except at exterior,
  almost the same), why? Smaller load is
  transferred to column directly
• Exterior moment increases for hidden, why?
  Exterior end is more restrained by column for
  hidden, thus more fixity and more moment.
• Do you expect problems in local practice? No,
  usually steel is provided at ve moment in
  detailing practice at the support beams are
  most of the time placed over masonry walls, so no
  stresses exist in them.
• Is it now necessary to change local practice?
  Yes, steel savings

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5.3 Two way slab systemsreview

• One-way Slab on beams suitable span 3 to 6m with
  LL 3-5kN/m2.
• Can be used for larger spans with relatively
  higher cost and higher deflections
• One-way joist system suitable span 6 to 9m with
  LL 4-6kN/m2.
• Deep ribs, the concrete and steel quantities are
  relatively low
• Expensive formwork expected.

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Flat Plate

• Flat Plate suitable span 6 to 7.5m with LL
  3-5kN/m2.
• Advantages
• Low cost formwork
• Exposed flat ceilings
• Fast
• Disadvantages
• Low shear capacity
• Low Stiffness (notable deflection)

179
5.5. Review Two way slab systemsFlat slab
Flat Slab suitable span 6 to 9m with LL
4-7.5kN/m2. Advantages Low cost formwork Exposed
flat ceilings Fast Disadvantages Need more
formwork for capital and panels
180
Waffle Slab

• Waffle Slab suitable span 9 to 14.5m with LL
  4-7.5kN/m2.
• Advantages
• Carries heavy loads
• Attractive exposed ceilings
• Fast
• Disadvantages
• Formwork with panels is expensive
• The two-way ribbed slab and waffled slab system
  General thickness of the slab is 5 to 10cm.

181
Two-way slab with beams

• Two-way slab with beams

182
Two-way slab behavior
ws load taken by short direction wl load taken
by long direction dA dB
Rule of Thumb For B/A gt 2, design as one-way slab
183
Analogy of 2-way slab to plank- beam floor
Section A-A Moment per m width in planks Total
Moment
184
Analogy of 2-way slab to plank- beam floor
Uniform load on each beam Moment in one beam
(Sec B-B)
185
Two-Way Slab Design
Total Moment in both beams Full load was
transferred east-west by the planks and then was
transferred north-south by the beams The same is
true for a two-way slab or any other floor system.
186
Equivalent Frames
Transverse equivalent frame
Longitudinal equivalent frame
187
General Design Concepts
(1) Direct Design Method (DDM)
Limited to slab systems to uniformly distributed
loads and supported on equally spaced columns.
Method uses a set of coefficients to determine
the design moment at critical sections as long as
two-way slab system meet the limitations of the
ACI Code 13.6.1.
188
Minimum Slab Thickness for Two-way Construction
ACI Code 9.5.3 specifies min. thickness to
control deflection. Three empirical limitations
based on experimental research are necessary to
be met
(a) For
fy in MPa. But h not less than 12.5cm
189
Minimum Slab Thickness for Two-way Construction
(b) For
fy in MPa. But h not less than 9cm.
(c) For
Use table 9.5(c) in ACI code
190
Minimum Slab Thickness for two-way construction
The definitions of the terms are
h Minimum slab thickness without interior
beams
ln b afm
Clear span in long direction measured face to
face of beam or column ratio of the long to short
clear span average value of af for all beams on
sides of panel.
191
Beam and Slab Sections for calculation of a
192
Beam and Slab Sections for calculation of a
Definition of beam cross-section, Charts used to
calculate a
Slabs without drop panels meeting 13.3.7.1 and
13.3.7.2, hmin 12.5cm Slabs with drop panels
meeting 13.3.7.1 and 13.3.7.2, hmin 10cm
193
Two way slab Example 1

• Analyze and design (as a two way slab without
  beams) the following one story structure (3.6m
  height) using 3D model (figure next page)
• Specifications B350, fy4200 kg/cm2,
  superimposed 50 kg/m2 , live loads 350 kg/m2,
  column dimensions 50cmX50cm

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solution

• Slab
• h550/3018.33cm , use 20cm
• wd (0.22.50.05).55t/m2, wl 0.35t/m2
• wu1.2.551.60.351.22t/m2
• Mo 1.226(5.5)2 /827.7t.m
• Mo- 0.6527.718t.m., Mo 9.7t.m.,
• (Mo-)c.s.0.751813.5t.m. (13.5/34.5t.m/m),
• (Mo-)m.s.0.25184.5t.m. (4.5/31.5t.m/m),
• (Mo )c.s 0.69.75.8t.m. (5.8/31.9t.m/m),
• (Mo )m.s 0.49.73.9t.m. (3.9/31.3t.m/m),

196
Verify equilibriumEtabs output
197
Verify stress-strain relationshipsmesh each 1m
198
Column strip -ve kN.m
199
Middle strip -ve kN.m
200
Two way slabsExample 2

• Analyze and design (as a two way slab with beams)
  the previous one story structure Specifications
  B350, fy4200 kg/cm2, superimposed 50 kg/m2,
  live loads 350 kg/m2, beam 30cm width by 50cm
  depth, column dimensions 50cmX50cm,

201
Solution

• h550/3615.3cm , use 20cm. Beam use 30cm50cm
  depth (ignore additional weight of beam)
• wd (0.22.50.05).55t/m2, wl 0.35t/m2
• wu1.2.551.60.351.22t/m2
• Mo 1.226(5.5)2 /827.7t.m
• Mo- 0.6527.718t.m., Mo 9.7t.m.,
• Ib 510-3 m4, Is 410-3 m4, a1.25, al2 /l1
  1.25
• (Mo-)cs0.751813.5t.m. (2/2.10.95t.m/m,
  B11.5t.m)
• (Mo-)ms0.25184.5t.m. (4.5/31.5t.m/m),
• (Mo )cs 0.759.77.3t.m(1.1/2.10.52t.m/m,
  B6.2t.m)
• (Mo )ms 0.259.72.4t.m. (2.4/30.8t.m/m),

202
Verify equilibriumEtabs output
203
Verify stress-strain relationshipsmesh each 1m
204
Bending moment in interior beam kN.m
205
Problem set 8

• Analyze and design (as a two way slab) the
  following one story structure (3.75m height)
  using 3D model (figure next slide)
• Specifications B350, fy4200 kg/cm2,
  superimposed 100 kg/m2 , live loads 200 kg/m2,
  column dimensions 35cmX35cm
• Slab without beams 14cm thickness
• Slab 14cm thickness, beams 35cm width by 55cm
  depth
• Slab 14cm thickness, beams 35cm width by 25cm
  depth

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5.4 Systems without vertical continuity

• Analyze a one story reinforced concrete structure
  (entertainment hall) made of one panel 50cm solid
  slab sitting on drop beams of 0.5m width and 1m
  depth supported on four square columns 50cm
  dimensions, 5m height and 15m span. The
  superimposed and live loads are 300kg/m2 and
  400kg/m2 respectively.

209
Example Model
210
Consider Design Alternatives

• The structural engineer is required to consider
  the following design alternative for the
  entertainment hall

211
Problem set 9

• Analyze the design alternative using local
  practice (slab-beam-column load path)
• Analyze the design alternative using 3D model
• C. Compare A and B
• D. Write a report to the client persuading him
  the validity of your findings

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5.5 General shape building systems

• Representation of ribs over slabs is usually
  inefficient modeling in general shape buildings.
  Another procedure is to use an equivalent solid
  slab of uniform thickness but preserving
• Stiffness ratios in both directions.
• Dead weight of slab.

214
General Shape buildingProblem set 10

• Floor system ribs 25cm
• Wall 20cm
• Superimposed 300kg/m2
• Live load 300kg/m2
• Econ2.20Mt/m2, density2.5t/m3
• Columns are rectangular 20cmX30cm

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Appendices

• Table 1604.5 IBC2009\ Occupancy category
• Table 1607.1 IBC2009\ Live load
• Table 9.5a ACI code
• Table 9.5c
• Table 12.15.2
• ACI 13.6.1 DDM limitations
• Fig. 13.3.8

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