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INTRODUCTION
1.1Advantages and Characteristics of Reinforced Concrete
Reinforced concrete is a composite material made of concrete and steel bars, see
Figure 1.1. It merges the advantages of concrete (form, stiffness and durability) with those of steel bars (high tensile strength and ductiltiy) into a single material with excellent physical and mechanical properties. Longitudinal steel in form of reinforcing bars is placed on the tension side of the member to carry flexural tensile stress from bending (in case of beams) or from combined axial laod and bending (in case of columns). Transverse steel in form of stirrups (in beams) or ties (in columns) serves to carry diagonal tension from shear forces.
Figure 1.1 Reinforced concrete as a composite material.
1.2Composite Action
For composite action to work, adequate load transfer between the steel bars and the surrounding concrete has to be ensured via adequate development length of the steel bars. As such, the steel bar will develop its full tension capacity (yield strength times the bar cross sectional area) before it pullls out of the concrete. That is why reinforcing bars are deformed (
Figure 1.2-a) to have adequate load transfer ability. Development length of straight bars ranges from 40-60 times the bar diameter. Using a 90 dgrees or 180 degrees hook (
Figure 1.2-b) at the end of the bar can reduce the development length by roughly 50%
Figure 1.2 Deformed reinforcing steel bars.
1.3Types of Reinforced Concrete Buildings
The most common types of low-rise and mid-rise (up to 20 stories) reinforced concrete buildings are:
Figure 1.3 RC Frame building.
Figure 1.4 RC wall building
Figure 1.5 Hybrid frame-wall building
1.4Floor Slabs
The choice of the type of floor slabs for buildings depends on many factors such as the material used for the load resisting system (steel, concrete, masonry, timber), vertical load intensity, span and panel aspect ratio. The thickness of the floor slab is a critical parameter that affect the weight and cost of the structure. This is particularly true for highrise buildings. For example, reducing the slab thickness from say 6.5 in. to 6.0 in. for 5000 sq. ft building with 30 stories will save 0.5 x 5000 x 30 = 75,000 cu ft of concrete. This reduction in weight will reduce the column loads and foundation loads. It will also reduce inertia forces from earthquakes.
Concrete is an excellent material for floor construction because of its high stiffness, fireproofing and good sound insulation properties. The selection of the floor system and the slab thickness is a key design parameter. The selection of the floor slab system depends on:
1- Clear span between columns or shear walls
2- Aspect ratio of the panel
3- Stiffness of boundary beams, if any
4- Load intensity
5- Function of the building
Figure 1.6 shows different types of floor slabs depending on span.
1.5Structural Safety and Reliability
There are three main reasons why safety factors should be incorporated in structural design:
1- Variability in resistance
. Variability of dimensions and locations of members
. Simplifying assumptions in design
3- Consequences of failure
. Potential loss of life
. Cost of replacement
. Cost of lost time and revenue
Figure 1.7 Examples of variability in strength and loads.
Figure 1.8 Safety margins.
Safety factors are based on a probabilistic approach. Safe and unsafe combinations of loading are shown in
Figure 1.8. The term Y=R-S in
Figure 1.8 is called safety margin. In this figure the shaded area represents the probability of failure. Because of economical reasons there will be always a very small probability of failure (typically 5%).
Reliability is the ability of a system or component to perform its required functions under stated conditions for a specified period of time. Reliability presents ways in which products fail, the effects of failure and aspects of design, manufacture, maintenance and use which affect the likelihood of failure.
Figure 1.8 shows the pressures that lead to the overall perception of risk. Reliability engineering has developed in response to the need to control these risks.
Figure 1.8 Perceived risk.
1.6Structural Analysis
The main objective of the analysis is to predict the response of buildings to loading. This can be measured by the resulting internal forces (axial force, shear force and bending moment) and deformations (deflections and rotations). Reinforced concrete frame structures are typically statically indeterminate. The following methods are used:
1- Approximate methods such as the portal frame method and the cantilever method
2- Classical methods for hand calculations such as the Moment Distribution Method
3- Stiffness method for computer applications. Many powerful commercial software codes are available such as STAAD and SAP.
4- ACI 318 shear and moment coefficients for continuous beams and one-way slabs.
1.6.1Effect of Continuity
For horizontal spanning from point A to B the location of the supports and consequently span/continuty effect has a dramatic influence on the demand/internal forces and deflections. As shown in
Fig. 1.9, for a simly supported beam AB the maximum moment at mid-span is wL2/8. If the support move to the inside, negative at the supports and positive moment at mid span develpe with values less than wL2/8. As the supports move close to the middle negative moment equal to wL2/8 develop. For a = 0.2L, equal negative and positive moments (0.02 wL2) develop leading to an optimum design.
Figure 1.9 Effect of continuity on beam moments.
1.6.2Effect of Boundary Conditions
As shown in
Fig. 1.10, the shape and maximum moments are affected by the boundary conditions at the supports. For a simply supported beam maximum moment of wL2/8 occurs at mid-span with maximum rotation θ= wL3/24 at the supports. For a fixed-fixed beam negative moment of wL2/12 develops at the supports with less positive moment of wL2/24 (compared to the simply supported case) at mid-span. In this case rotation is zero at the supports and maximum deflection is less comapred to the simply supported case. Por partil constraints at the supports the negative moment at the supports will be less than wL2/24 whereas the postive moment at mid-span will be greater than wL2/24.
Figure 1.10 Effect of boundary conditions on beam moments.
1.6.3Shear and Moment Cofficients for Continuious Beams and One-Way Slabs
Figure 1.11 shows ACI 318 shear and moment coefficients for continuous beams where moment is Cm wL2 and shear is Cv wL/2. It is assumed that live loads are not greater than three times the dead loads and therefore pattern loading is ignored (for LL/DL ratio less than or equal to 3.0) and the total full dead and live loads are considered.
1.6.4Pattern Loading
For heavy live loads that are more than three times the dead loads the effect of pattern loading should be accounted for. Ignoring the effect of pattern loading in this case would result in an underestimation of maximum moments and shear forces at the member ends. This effect will be more significant in case of long catilevers and dissimilar spans. Some computer codes/software consider the effect of pattern loading in the analysis of frames under vertical loads.
Figure 1.11 Shear and moment coefficients for continuous beams.
1.7Structural Design
1.7.1Objectives of Structural Design
The main objectives/goals of structural design are:
1- Adequate performance under service loads. This is referred to as “Serviceabilty limit state” and it concerns with deflection limits, vibration control and crack control.
2- Adequate factor of safety against failure/collapse in case of overloading.
3- Economy (initial and long-term).
1.7.2Design Loads
Gravity Loads (dead and live loads) for beams and columns can be calculated using the concept of tributary area, see
Figure 1.12. Note that the loads on beams are localized whereas the axial loads on columns are accumulative (maximum axial load on ground floor columns). Shear and moments on columns are localized at each floor levels since the beam moments on the joints are balanced by colums at top and bottom of each joint.
Lateral loads from...