Basic rules for design of beam:-
1. Effective span:- In the case of simply supported beam the effective length,
L = i. Distance between the centre of support
ii. Clear span + eff. Depth
eff. Span = least of i. & ii.
2. Effective depth:- The normal distance from the top edge of beam to the centre of tensile reinforcement is called effective depth. It is denoted by ‘d’.
d= D- effect. Cover
where D= overall depth
3. Bearing :- Bearings of beams on brick walls may be taken as follow:
- Up to 3.5 m span, bearing = 200mm
- Up to 5.5 m span, bearing =300mm
- Up to 7.0 m span, bearing =400mm
4. Deflection control:- The vertical deflection limits assumed to be satisfied if (a) For span up to 10m
Span / eff. Depth = 20
(For simply supported beam)
Span / eff. Depth = 7
(For cantilever beam)
(b) For span above 10m, the value in (a) should be multiplied by 10/span (m), except for cantilever for which the deflection calculations should be made.
(c) Depending upon the area and type of steel the value of (a&b) modified as per modification factor.
5. Reinforcement :-
(a) Minimum reinforcement:- The minimum area of tensile reinforcement shall not be less than that given by the following:
Ast = 0.85 bd / fy
(b)Maximum reinforcement:- The maximum area of tensile reinforcement shall not be more than 0.4bD
(c)Spacing of reinforcement bars:-
i. The horizontal distance between to parallel main bars shall not be less than the greatest of the following:
- Diameter of the bar if the bars are of same diameter.
- Diameter of the larger bar if the diameter are unequal.
- 5mm more than the nominal maximum size of coarse aggregate.
ii. When the bars are in vertical lines and the minimum vertical distance between the bars shall be greater of the following:
- 15mm.
- 2/3rd of nominal maximum size of aggregate.
- Maximum diameter of the bar
6. Nominal cover to reinforcement :- The Nominal cover is provided in R.C.C. design:
- To protect the reinforcement against corrosion.
- To provide cover against fire.
- To develop the sufficient bond strength along the surface area of the steel bar.
As per IS 456-2000, the value of nominal cover to meet durability requirements as follow:-
Exposure conditions
|
Nominal cover(mm)
Not less than
|
Mild
Moderate
Severe
Very severe
Extreme
|
20
30
45
50
75
|
Procedure for Design of Singly Reinforced Beam by Working Stress Method
Given :
(i) Span of the beam (l)
(ii) Loads on the beam
(iii)Materials-Grade of Concrete and type of steel.
1. Calculate design constants for the given materials (k, j and R)
k = m σcbc / m σcbc + σst
where k is coefficient of depth of Neutral Axis
j = 1- k/3
where j is coefficient of lever arm.
R= 1/2 σcbc kj
where R is the resisting moment factor.
2. Assume dimension of beam:
d = Span/10 to Span/8
Effective cover = 40mm to 50mm
b = D/2 to 2/3D
3. Calculate the effective span (l) of the beam.
4. Calculate the self weight (dead load) of the beam.
Self weight = D x b x 25000 N/m
5. Calculate the total Load & maximum bending moment for the beam.
Total load (w) = live load + dead load
Maximum bending moment, M = wl2 / 8 at the centre of beam for simply supported beam.
M = wl2 / 2 at the support of beam for cantilever beam.
6. Find the minimum effective depth
M = M
= Rbd2
dreqd. = √ M / R.b
7. Compare dreqd. With assumed depth value.
(i) If it is less than the assumed d, then assumption is correct.
(ii) If dreqd. is more than assumed d, then revise the depth value and repeat steps 4, 5 & 6.
8. Calculate the area of steel required (Ast).
Ast = M / σst jd
Selecting the suitable diameter of bar calculate the number of bars required
Area of one bar = π/4 x φ2 = Aφ
No. of bars required = Ast /Aφ
9. Calculate minimum area of steel (AS) required by the relation:
AS = 0.85 bd / fy
Calculate maximum area of steel by the area relation:
Maximum area of steel = 0.04bD
Check that the actual ASt provided is more than minimum and less than maximum required.
10. Check for shear and design shear reinforcement.
11. Check for development length.
12. Check for depth of beam from deflection.
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