Presentation on

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:

longitudinal reinforcement is placed

closed to the bottom side of the beam

Concrete is good in compression and bad in tension.

Tensile strength of concrete is about 1/10 of f’c.

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

Fig: Steel stress-strain curve Fig: Concrete stress-strain curve

Both of the material’s stress is proportional to strain

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

Singly reinforced beam :

Strain compatibility:

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.

Resisting Moment:

Strain compatibility :

ACI recommended that f’s be

equal to twice this value

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.

Advantages 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.

Disadvantages of Using WSD

method