Test: Limit State of Collapse: Flexure - Civil Engineering (CE) MCQ

Working stress method is based on calculations on service load conditions alone. Ultimate Strength method is based on calculations on ultimate load conditions alone. In Limit State method, safety at ultimate loads and serviceability at working loads are considered.

The assumption made according to IS 456 in limit states of collapse are:

• Plane section normal to the axis remains plane after bending.
• The maximum strain in the concrete at the outermost compression fiber can be taken as 0.0035 in bending.
• The tensile strength of the concrete is ignored.
• The relationship between stress-strain distribution in concrete is assumed to be parabolic.

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Hence, Maximum stress in concrete by code is restricted to 0.67f_ck.

Acceptable limits for safety and serviceability requirements before failure occurs is called limit state. In Limit State design, structures are designed on the basis of safety against failure and are checked for serviceability requirements.

There are three design methods for the reinforced concrete structures.

• Working Stress Method: 
  This is the traditional design method in which the materials are assumed to behave in a linearly elastic manner and stress in materials are not allowed to exceed the permissible stress under working loads. The structures designed using WSM are uneconomical as they do not consider the non-linear portion of the stress-strain curve.
• Limit State Method: 
  This method considers the uncertainties in the load and material properties and makes a probabilistic estimation of partial safety factors. Limit state is the state at which structure becomes unfit for use.
  There are two limit states:
  • Limit state of serviceability:e.g Deflection, crack width, Vibration, Leakage etc.
  • Limit state of collapse:e.g Flexure, Compression, Shear, Torsion, Buckling, Overturning etc.
• Ultimate load method: 
  In this method stress condition at the stage of impending failure of any section is analyzed and non-linear stress-strain curve of steel and concrete are used.
  

Limit state method uses multiple safety factor format that helps to provide adequate safety at ultimate loads and adequate serviceability at service loads, by considering all possible limit states. Multiple safety factor format is also called partial safety factor format.

Values of the factor of safety (partial) for load combination:

Where, DL = Dead load, LL = Live load WL = Wind load EL = Earthquake load
Calculation:
Given: Dead load (DL) = 20 KN and Live load (LL) = 12 kN
Partial factor of safety = 1.5 (DL + LL) = 1.5 (20 + 12) = 48 kN
Additional Information
Values of the factor of safety (partial) for load combination:

Limit state of strength are prescribed to avoid collapse of structure which may endanger safety of life and property. It includes (i) loss of equilibrium of whole or part of structure, (ii) loss of stability of structure as a whole or part of structure, (iii) failure by excessive deformation, (iv) fracture due to fatigue , (v) brittle fracture.