Limit State Method Of Design | Reinforced Cement Concrete | CE

Deflection limits:

Final deflection .

Final deflections due to partitions and finishes or 20 mm whichever is less

For calculating deflections, take

E = Ec = 5000

and I = I

eff =

but I

r £ I

eff < Igr

.

where Mr = fcr

.

Igr = M.I. of gross section

I

r = M.I. of cracked section.

For singly reinforced sections,

I

r = + m Ast

(d – x)

2

where x = distance of NA from compression flange

For doubly reinforced sections

I

r = + (m – 1) Ast

(d – d)

2 + m Ast

(d – x)

2

* Crack width:

Acceptance limits are:

1. 0.3 mm in members if cracking is not harmful to the durability of structure.

2. 0.2 mm in members continuously exposed to moisture or in contact with soil.

3. 0.1 mm in aggressive environment.

* Cracks due to bending in a compression member subjected to axial load of 0.2 fck Ac need not be

checked, if

1. Spacing between adjacent bars > dia. of larger bar

and 5 mm more than size of coarse aggregate

2. If there are two or more number of rows of bars the spacing between the rows should be larger

of the following.

(a) 15 mm

(b) × nominal size of aggregates

(c) Size of bar

* Crack width may be calculated from the following formula:

Wcr =

where acr = Distance of the point from the surface of nearest longitudinal bars

Cmin = Minimum cover to the longitudinal barem = Average strain in longitudinal bar

h = Overall depth of the section

x = Depth of NA from compression edge

Design of Beams

* Effective span

1. Simply supported beams or slabs

leff = Clear span + Effective depth or centre-to-centre distance between the supports

whichever is less

2. Continuous beams or slabs

(a) If width of support, w < × clear span, the effective span is same as for simply supported

case

(b) For end span with one end simply supported and the other end continuous.

leff = Clear span + d or

= Clear span + Width of support whichever is less.

3. In case of roller supports,

leff = distance between the supports

4. Cantilevers:

leff = Clear span + d/2

5. Overhanging beams:

leff = Centre of support to free end.

6. Frames:

leff = Centre-to-centre distance.

Size of Beam

* If we select depth of beam th to th of span for simply supported beams and th to th of span

for continuous beams. Normally, it will be under reinforced and do not violate deflection criteria.

From the consideration of standardizing form works, overall depth is kept in multiples of 50 mm

usually 250 mm to 700 mm in multiples of 50 mm.

* The width is normally kept as 200 mm, 250 mm, 300 mm and 350 mm. Use of 230 mm is also

practised where 230 mm (9≤) brick walls are built.

Cover to Reinforcement

Minimum nominal cover to meet durability requirements as per IS 456 are:

Exposure condition Minimum cover

Mild 20 mm

Moderate 30 mm

Severe 45 mm

Very severe 50 mm

Extreme 75 mm