Reinforced Concrete is a composition of concrete and rebar steel. The compressive strength of concrete and tensile capacity of steel makes it an excellent building material. Concrete is a brittle material which fails without any warning, while steel behaves as ductile material up to yield point thus the composite of two material will work together to carry loads and withstand any force against the concrete structure.
Basically, steel follows the Hooke’s law, it remains elastic till yield point. Elasticity is the property of a material to retain its original state after the force is removed. Once the steel enters in its yielding state, deformations became plastic. That is it will not it retain its original position after removal of the force. Yielding is the warning before it reaches the ultimate point of failure.
It is preferred to design a reinforced concrete section such that the steel reinforcement yield first before concrete reached its strain limit. There are three different design philosophies of reinforced concrete design that are adopted practically:
1. Working Stress Design
This is the oldest design approach. Working stress design is also known as Allowable Stress Design (ASD). In this method, only elastic limit of the material is utilized in the design. Linear elastic stresses and strains are easy to understand and evaluate.
In working stress design method, member sizes are workout such that it would not even reach the yield point. This approach gives relatively large sizes and underutilizes the capacities. This is the uneconomical and unrealistic approach to design. Refer Stress – Stain Diagram below.
Definition of Stress, δ and Strain, ε
Stress is force per unit area that results from an applied load
Strain is a physical deformation response of a material to stress.
Concrete is 0.45 f’c
Steel is 0.60 fy
2. Ultimate Stress Design
Ultimate stress design is also known as Strength Design Method. It considers the plastic limit of stresses in design. Sections are designed such that the stress may reach till ultimate point. The non-linear behavior of the material is a bit difficult to estimate, but this is the realistic approach. It considered the stresses due to bending in design. Ultimate stress design gives significantly small sizes of member which leads to economy in design.
3. Limit State Method
Limit state method is the combination of:
Working Stress Design/ Allowable Stress Design
Ultimate Stress Design/ Strength Design Method
In this method of design Ultimate Design strategy is adopted for strength design such as flexure, shear, bending, creep and fatigue etc. Members are designed such that materials reach its ultimate point. Since the plastic limit is considered in the design, chances are the development of more cracks and deflection. So the serviceability of structure has to be checked against working stresses. Serviceability includes drifts, deflections and cracks widths.
Limit State method is the practically used method of design. First, we analyze the building drifts for allowable stresses. Structural members are designed for ultimate stresses. Next, we check member deflection and crack width for service loads. If they exceed the limit, we increase size or reinforcement, despite the fact, it passes the strength design.
Usually, for the design of the water retaining structure, allowable crack width is so small. In such structures, working stress design governs over the ultimate design method. We need to provide more thickness or closely spaced bars to overcome cracking. Building foundations are also sized using working stress method.