Rectangular beam design by WSD method (singly & doubly reinforcement)

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Rectangular beam design :
singly and doubly reinforced
beam by WSD

What is a Beam?
 A Beam is any structural member which resists load mainly
by bending. Therefore it is also called flexural member. Beam
may be singly reinforced or doubly reinforced. When steel is
provided only in tensile zone (i.e. below neutral axis) is called
singly reinforced beam, but when steel is provided in
tension zone as well as compression zone is called doubly
reinforced beam.

Necessity of reinforcement in
beam:
Concrete is good in compression and bad in tension.
Tensile strength of concrete is about 1/10 of f’c.

longitudinal reinforcement is placed
closed to the bottom side of the beam

Behaviour of a beam under loads

RCC design methods:
RCC design
method

USD
method

WSD
method

Working stress design method
(WSD)
 This design concept is based on elastic theory, assuming a straight line
stress distribution along the depth of the concrete. Concrete response
elastically upto compressive strength not exceeding about ½ of its
strength, while steel remains elastic practically upto yield strength. So, in
practically, allowable stresses are set at about ½ the concrete compressive
strength and ½ the yield stress of steel.
 The concrete remain elastic at ½×f’c which range to strain of about 0.0005
and the steel is elastic near to it’s yield point or strain of 0.002.
 According to ACI code the value is equal to 0.45× f’c .

Assumptions:
1) Section remains plane
2) Stress proportioned to Strain
3) Concrete not take tension
4) No concrete-steel slip

Both of the material’s stress is proportional to strain

Fig: Concrete stress-strain curve

Fig: Steel stress-strain curve

Design Conditions:

1) Stress elastic and sections uncracked:
Tensile strength of concrete fct <Modulus of rupture fr
Compressive stress of concrete fc << ½ f’c
Tensile stress in steel fs < fy yield strength of steel

2) Stress elastic and section cracked:
Tensile strength of concrete fct > Modulus of rupture fr
Compressive stress of concrete fc < ½ f’c
Tensile stress in steel fs < fy yield strength of steel

Doubly reinforced beam :
If concrete section cannot develop the required compressive force to resist the
maximum bending moment then additional reinforcement is added in the
compression.

Strain compatibility :

ACI recommended that f’s be
equal to twice this value

Advantages of Using WSD
method
Following are some advantages of Allowable stress design method

• Elastic analysis for loads become
compatible for design.
• Old famous books are according to this
method.
• Experienced engineers are used to this
method.
• In past it was the only method for design
purposes.
• This method is included in AISC-05
specifications as an alternate method.

Disadvantages of Using WSD
method
• Latest research and literature is very
limited.
• Same factor of safety is used for
different loads.
• Failure mode is not directly predicted.
• With some overloading, the material
stresses increase but do not go to
collapse.
• The failure mode can not be observed.
• The warning before failure cannot be
studied precisely.
• Results cannot be compared with
experimental tests up to collapse.

Rectangular beam design by WSD method (singly & doubly reinforcement)

Rectangular beam design by WSD method (singly & doubly reinforcement)

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Rectangular beam design by WSD method (singly & doubly reinforcement)