# Working Stress Design Method

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2 Working Stress Design Method (Refer IS800:1984)

2.1 Basic Assumptions in Working Stress Design

Philosophy of working stress design is based on the assumption that the material of the structure behaves elastically throughout the service period. In this method deformation due to applied load is assumed to be small and load – deformation relationship is taken linear. In working stress design, a transverse section of structural member is considered to be plain after stressing.

In this method, structure are analysed for worst combination of service loads and structural members are proportioned for the permissible stresses of materials.

2.2 Service load and Permissible Stress

Service load

The load expected to act on a structure during its service life is characteristic load. Characteristic load is taken as service load. Characteristic value of load is based on the statistical data. Characteristic load has 95% probability of not being exceeded during the life time of the structure.

Permissible stress

Maximum stress that is permitted to be experienced in the elements, members or structure under service load is permissible stress. Permissible stress is also termed as working stress or allowable stress. The permissible stress is assessed with reference to yield stress of material. Permissible stress is found out by dividing yield stress by factor of safety [Permissible Stress = Yield Stress/ Factor of Safety]. For design purpose, permissible stresses of materials are taken as specified by the code of practice.

Factor of safety

Factor by which strength of material is reduced in design is called factor of safety. Factor of safety considers

• Possibility of overloading on the structure

• Adverse impact of approximation adopted in structural analysis

• Undesirable effect due to residual stress and stress concentration

• Under run of mechanical and physical properties of material

• Under run of geometric dimensions of members

• Effect of the quality of workmanship and other uncertainties

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Value of factor of safety depends on the importance of structural member, nature of loads and its behaviour.

2.3 Design in tension, compression, bending and shear

Design in Tension

In structural member subjected to tensile force, the tensile stress on its net sectional area shall not exceed permissible tensile stress.

????≤?????

Design in Compression

In structural member subjected to compressive force, the compressive stress on its effective sectional area shall not exceed permissible compressive stress.

????≤?????

????− ?????????????? ? ??? ????? ???? ??????? ? ????? ?

Where,

????? – Permissible tensile stress

????? = 0.6????

???? – Yield stress

????= T / Anet

Anet – Net sectional area of tension member

T – Tensile Force

????− ??? ??? ? ??? ????? ???? ??????? ? ????? ?

Where,

????? – Permissible compressive stress

????? ≤ 0.6????

???? – Yield stress

Permissible compressive stress depends on the slenderness ratio and grade of steel of compression member.

Slenderness Ratio = l/r

l- Effective length of compression member

r- Radius of gyration of compression member

????= C / Ae

Ae – Effective sectional area of compression member

C – Compressive Force

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Design in Bending

In structural member subjected to bending, the maximum bending stress in tension and compression shall not exceed permissible bending stress in tension and compression.

????≤????? and ????≤?????

Design in Bearing

In structural member subjected to local compressive stress (bearing stress), the bearing stress shall not exceed permissible bearing stress. ??? ≤???

????− ??? ? ?? ? ??? ????? ???? ??????? ? ????? ?

Where,

????? – Permissible bending stress in compression

????? ≤ 0.66????

???? – Yield stress

Permissible bending stress in compression depends on the ratio of D/T, l/r, T/tw, d1/tw and grade of steel.

D – Depth of beam

T – Thickness of flange

l – Effective length of compression flange

tw – Thickness of web of beam

d1 – Effective depth of web

r- Minimum radius of gyration

????? – Permissible bending stress in tension

????? = 0.66????

???? – Yield stress

????= M / Z

Z – Section Modulus of flexure member

M – Bending Moment

Where,

??? – Bearing stress due to applied ? ????? load

??? = C / Bearing area

C – Compressive force

??? – Permissible bearing stress

??? = 0.75fy

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Design in Shear

In structural member subjected to shear, the maximum shear stress shall not exceed permissible shear stress.

??? ≤???

Where,

??? – Shear stress due to applied ? ????? load

??? = V/Dtw

V – Shear force

D – Depth of beam

tw – Thickness of web

??? – Permissible shear stress

??? ≤ 0.4fy

Permissible shear stress depends on whether the plate is stiffened or not

??? = 0.4fy for unstiffened beam

??? ≤ 0.4fy for stiffened beam and depends on the thickness of plate and spacing of stiffeners