Lecture 2 - Fundamentals September, 2011 CE 370

Lecture Goals Design Process Limit states Design Philosophy Loading

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

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

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

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

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

Limit States and 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 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 States Ultimate limit state Rupture of critical components causing partial or complete collapse. (flexural, shear failure).

Ultimate Limit States 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

Ultimate Limit States 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).

Serviceability Limit States 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.

Serviceability Limit States 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

Serviceability Limit States 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

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

Special Limit States Damage/failure caused by abnormal conditions or loading. Extreme earthquakes damage/collapse Floods damage/collapse

Special Limit States 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

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

Limit States Design Consider the significant limits states. Members are designed for ultimate limit states Serviceability is checked. Exceptions may include  water tanks (crack width)  monorails (deflection)

ACI Building Codes 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.

Design Philosophy 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.

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.

Strength Design Method 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.

Safety Provisions Structures and structural members must always be designed to carry some reserve load above what is expected under normal use.

Safety Provisions 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 in Resistance 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.

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

Loading 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

Loading 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- 98) – has been updated to ASCE 7-02.

Dead Loading Dead Loading Weight of all permanent construction Constant magnitude and fixed location

Dead Loads 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

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.

Live Loads See Table 2-1 from ASCE 7-98 Stairs and exitways: 100 psf Storage warehouses:125 psf (light) 250 psf (heavy) Minimum concentrated loads are also given in the codes.

Live Loads

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

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

Classification of Buildings for Wind, Snow and Earthquake Loads 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

Classification of Buildings for Wind, Snow and Earthquake Loads Based on Use Categories (I through IV) Buildings/structures designated essential facilities (hospitals, fire and police stations, communication centers, power-generating stations) IV

Snow Loads 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 Loads Wind pressure is proportional to velocity squared (v 2 ) Wind velocity pressure = q z

Wind Loads where 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) K z = Exposure coefficient (bldg. ht., roughness of terrain) k zt = Coefficient accounting for wind speed up over hills I = Importance factor

Wind Loads Design wind pressure, p = q z * G * C p G =Gust Response Factor C p =External pressure coefficients (accounts for pressure directions on building)

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

Earthquake Loads Inertia forces caused by earthquake motion. Equivalent Static Force Procedure for example, in ASCE 7-95: V = C s * W where V =Total lateral base shear C s = Seismic response coefficient W =Total dead load

Earthquake Loads Total Dead Load, W: 1.0 * Dead Load * Storage Loads + larger of partition loads or 10 psf + Weight of permanent equipment + contents of vessels + 20% or more of snow load

Earthquake Loads where C v =Seismic coefficient based on soil profiled and A v C a =Seismic coefficient based on soil profiled and A a R = Response modification factor (ability to deform in inelastic range) T =Fundamental period of the structure

Earthquake Loads where T =Fundamental period of the structure T = C T h n 3/4 where C T = for MRF of concrete for other concrete buildings. h n =Building height

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:  Rain water ponds in area of maximum deflection  increases deflection  allows more accumulation of water  cycle continues…  potential failure

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

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

w P1P1 P2P2 P3P3 C T jd  cm  tm ) a) Flexural stresses on a cross section Internal couple. ) b) Internal couple. Basic Design Relationship:

The beam shown in the figure will safely support the load if, at every section, the resistance of the member exceed the effects of loads: R   S (2-1) The resistance, R is function of material and geometric properties. To allow for variability in computed resistance and load effects, eq. (2-1) is rewritten as :  R n   1 S 1 +  2 S 2 + … (2-1a)  is strength-reduction factor less than1  I is load factor greater than 1 R n stands for nominal resistance (based on specified material and geometric properties.) S stands for load effects (based on specified loads.) In terms of Moments:  M n   D M D +  L M L + … (2-2a) Similar equations can be written for shear, V, and axial forces, P:  V n   D V D +  L V L +... (2-2b)  P n   D P D +  L P L + … (2-2c) Equation (2-1) is the basic limit-states design equation. Equations (2-2a) to (2-2c) are special forms.

Strength design is a limit-state design (primarily based on ultimate limit-states.) ACI (SBC-304) sections 9.1.1, — Structures and structural members shall be designed to have design strengths at all sections at least equal to the required strengths calculated for the factored loads and forces in such combinations as are stipulated in this code — Members also shall meet all other requirements of this code to ensure adequate performance at service load levels. Art  design strength  required Strength design strength=  nominal strength, e.g.  M n,  V n, …. required strength=load effect resulting from factored loads, M u, V u, …. For Beam design, the design criteria become  M n  M u and  V n  V u M u = factored load moment, (Moment computed from combination of factored loads) V u = factored load shear, (Shear computed from combination of factored loads) 1.Strength Design Method in The ACI (SBC- 304) Code

Load Combinations (SBC 304 Section 9.2) U = 1.4(D + F ) (9-1) U = 1.4(D + F + T) + 1.7(L + H)+ 0.5(L r or R) (9-2) U = 1.2D + 1.6(L r or R) + (1.0L or 0.8W) (9-3) U = 1.2D + 1.6W + 1.0L + 0.5(L r or R) (9-4) U = 1.2D + 1.0E + 1.0L (9-5) U = 0.9D + 1.6W + 1.6H (9-6) U = 0.9D + 1.0E + 1.6H (9-7) D: dead load, L: Live load, Lr: roof live load, W: wind load, E: earthquake load, etc.

Strength Reduction Factors,  (SBC 304 Section 9.3) — Tension-controlled sections as defined in SBC 304 Sec (See also SBC 304 Sec ) — Compression-controlled sections, as defined in SBC 304 Sec : (a) Members with spiral reinforcement conforming to SBC 304 Sec (b) Other reinforced members — Shear and torsion