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Lecture 3 - Fundamentals

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Lecture 3 - Fundamentals

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Lecture 3 - Fundamentals

January 17, 2002

CVEN 444

- Design Process
- Limit states
- Design Philosophy
- Loading

- Phase 1: Definition of clients’ needs and priorities.
- Functional requirements
- Aesthetic requirements
- Budgetary requirements

- Phase 2: Development of project concept
- Develop possible layouts
- Approximate analysis preliminary members sizes/cost for each arrangement

- Phase 2: Development of project concept
- Selection most desirable structural system
- Appropriateness
- Economical/Cost
- Maintainability

- Selection most desirable structural system

- Phase 3: Design of individual system
- Structural analysis (based on preliminary design)
- Moments
- Shear forces
- Axial forces

- Structural analysis (based on preliminary design)

- Phase 3: Design of individual system(cont.)
- Member design
- Prepare construction days and specifications.
- Proportion members to resist forces
- aesthetics
- constructability
- maintainability

- Member 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

- Ultimate
- Serviceability
- Special

Ultimate limit state

- structural collapse of all or part of the structure ( very low probability of occurrence) and loss of life can occur.
- Loss of equilibrium of a part or all of a structure as a rigid body (tipping, sliding of structure).

Ultimate limit state

- Rupture of critical components causing partial or complete collapse. (flexural, shear failure).

- Progressive Collapse
- Minor local failure overloads causing adjacent members to failure entire structure collapses.
- Structural integrity is provided by tying the structure together with correct detailing of reinforcement provides alternative load paths in case of localized failure

- Formation of a plastic mechanism - yielding of reinforced forms plastic hinges at enough sections to make structure unstable.
- Instability cased by deformations of structure causing buckling of members.
- Fatigue - members can fracture under repeated stress cycles of service loads (may cause collapse).

- Functional use of structure is disrupted, but collapse is not expected
- More often tolerated than an an ultimate limit state since less danger of loss of life.
- Excessive crack width leakage corrosion of reinforcement gradual deterioration of structure.

- More often tolerated than an an ultimate limit state since less danger of loss of life.
- Excessive deflections for normal service caused by possible effects
- malfunction of machinery
- visually unacceptable

- Excessive deflections for normal service caused by possible effects

- More often tolerated than an an ultimate limit state since less danger of loss of life.
- Excessive deflections for normal service caused by possible effects
- damage of nonstructural elements
- changes in force distributions
- ponding on roofs collapse of roof

- Excessive deflections for normal service caused by possible effects

- More often tolerated than an an ultimate limit state since less danger of loss of life.
- Undesirable vibrations
- vertical floors/ bridges
- lateral/torsional tall buildings
- Change in the loading

- Undesirable vibrations

Damage/failure caused by abnormal conditions or loading.

- Extreme earthquakes damage/collapse
- Floods damage/collapse

Damage/failure caused by abnormal conditions or loading.

- Effects of fire,explosions, or vehicular collisions.
- Effects of corrosion, deterioration
- Long-term physical or chemical instability

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

- Consider the significant limits states.
- Members are designed for ultimate limit states
- Serviceability is checked.
Exceptions may include

- water tanks (crack width)
- monorails (deflection)

Whenever two different materials , such as steel and concrete, acting together, it is understandable that the analysis for strength of a reinforced concrete member has to be partial empirical although rational. These semi-rational principles and methods are being constant revised and improved as a result of theoretical and experimental research accumulate. The American Concrete Institute (ACI), serves as clearing house for these changes, issues building code requirements.

- Two philosophies of design have long prevalent.
- Working stress method focuses on conditions at service loads.
- Strength of 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.

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.

Strength provide 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 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.

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.

- 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.

Comparison of measured and computed failure moments based on all data for reinforced concrete beams with fc > 2000 psi.

Frequency distribution of sustained component of live loads in offices.

A number of subjective factors must be considered in determining an acceptable level of safety.

- Potential loss of life.
- Cost of clearing the debris and replacement of the structure and its contents.
- Cost to society.
- Type of failure warning of failure, existence of alternative load paths.

The distributions of the resistance and the loading are used to get a probability of failure of the structure.

The term

Y = R - S

is called the safety margin. The probability of failure is defined as:

and the safety index is

SPECIFICATIONS

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.

Loadings in these codes are mainly based on ASCE Minimum Design Loads for Buildings and Other Structures (ASCE 7-95) – has beenupdated to ASCE 7-98.

- 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.)

Can Be Uncertain….

- pavement thickness
- earth fill over underground structure

- 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.

See Table 2-1 from ASCE 7-95

Stairs and exitways: 100 psf

Storage warehouses:125 psf (light)250 psf (heavy)

Minimum concentrated loads are also given in the codes.

ASCE 7-95 allows reduced live loads for members with influence area (AI) of 400 sq. ft. or more:

where Lo 0.50 Lo for members supporting one floor

0.40 Lo otherwise

AI determined by raising member to be designed by a unit amount. Portion of loaded area that is raised = AI

Beam: AI = 2 * tributary area

Column:AI = 4 * tributary area

Two-Way Slab:AI = panel area

(see Fig. 2-10, text)

Load Reduction

- Snow Loads
- Earthquake
- Wind
- Soil Pressure
- Ponding of Rainwater
- Temperature Differentials

Based on Use Categories (I through IV)

III

Buildings and other structures that represent a low hazard to human life in the event of a failure (such as agricultural facilities)

Buildings/structures not in categories I, III, and IV

Based on Use Categories (I through IV)

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)

III

Based on Use Categories (I through IV)

Buildings/structures designated essential facilities (hospitals, fire and police stations, communication centers, power-generating stations)

IV

The coefficients of snow loads are defined in weight.

Ground Snow Loads (Map in Fig. 6, ASCE 7):

- 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

- Wind pressure is proportional to velocity squared (v2 )
- Wind velocity pressure = qz

where

0.00256 reflects mass density of air and unit conversions.

V =Basic 3-second gust wind speed (mph) at a height of 33 ft. above the ground in open terrain. (1:50 chance of exceedance in 1 year)

Kz = Exposure coefficient (bldg. ht., roughness of terrain)

kzt = Coefficient accounting for wind speed up over hills

I = Importance factor

Design wind pressure,

p = qz * G * Cp

G =Gust Response Factor

Cp =External pressure coefficients (accounts for pressure directions on building)

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

Inertia forces caused by earthquake motion. Equivalent Static Force Procedure for example, in ASCE 7-95:

V = Cs * W

where

V =Total lateral base shear

Cs = Seismic response coefficient

W =Total dead load

Total Dead Load, W:

1.0 * Dead Load

+ 0.25 * Storage Loads

+ larger of partition loads or 10 psf

+ Weight of permanent equipment

+ contents of vessels

+ 20% or more of snow load

where

Cv =Seismic coefficient based on soil profile and Av

Ca =Seismic coefficient based on soil profiled and Aa

R = Response modification factor (ability to deform in inelastic range)

T =Fundamental period of the structure

where

T =Fundamental period of the structure

T = CT hn3/4

where CT = 0.030 for MRF of concrete

0.020 for other concrete buildings.

hn =Building height

- Ponding of rainwater
- Roof must be able to support all rainwater that could accumulate in an area if primary drains were blocked.
- Ponding Failure:
Rain water ponds in area of maximum deflection

increases deflection

allows more accumulation of water cycle continues… potential failure

- Roof loads are in addition to snow loads
- Minimum loads for workers and construction materials during erection and repair

- Construction materials
- Weight of formwork supporting weight of fresh concrete