DESIGN OF (RCC)
LIMIT STATE Method
Now all the structural design is totally based on Limit State Method.
The acceptable limit for the safety and serviceability purpose requirement before failure occurs of structures is called Limit State.
There are two types of Limit state
- Limit state of collapse
We need to find the following listed parameter,
§Flexure (Bending)
§Shear of member
§Compression of member
§Torsion on member
- Limit state of serviceability
We need to find the following parameter,
§Deflection of structure or member
§Vibration of structure
§Cracking occurs in structure
- CHARACTERSTIC COMPRESSIVE STRENGTH of Concrete
The value of strength of material, below which not more than 5% of test results are expected to fall of concrete.
Grade of Concrete | fck (N/mm2) |
M 20 | 20 |
M 25 | 25 |
M 30 | 30 |
Steel | fy (N/mm2) |
Mild steel Fe-250 | 250 |
HYSD steel Fe-415 | 415 |
Cold twisted bar Fe-500 | 500 |
- Characteristic Load: The value of load which has 95% probability of not being exceed during life of structural member.
- PARTIAL SAFETY FACTOR
- Due to reasons, of strength of structure get reduced. The Design strength of the material obtained by applying safety factor to the strength.
- In case of Concrete, γm = 1.50.
- In case of Steel, γm = 1.15.
- Tensile or Flexural Strength = 0.7 √fck
- Compressive Strength = 0.446 fck
- Punching Strength = 0.25 √fck
- Bearing Strength = 0.6 fck
- MODULUS OF ELASTICITY
- In case of Mild Steel, Es = 2 x 105 N/mm2
- In case of Concrete, Ec = 5000 √fck
- M-20
- M = Mix
- 20 = 20 N/mm2 compressive strength at 28 days.
UNDER REINFORCED SECTION
- Steel quantity is less compared to balanced section.
- Tensile stress in steel achieve limiting value earlier to compressive stress in concrete reaches the limiting value.
- Steel strength fails before concrete strength.
BALANCED SECTION
- Compressive stress/strain in concrete and tensile stress/strain in steel reach their limiting value simultaneously.
- Both materials steel and concrete fail at same time.
OVER REINFORCED SECTION
- Compressive stress/strain in concrete reaches limiting value earlier to tensile stress/strain in steel.
- Concrete fails before steel.
- Reinforcement percentage is more compared to balanced section of structure.
Value of Yield Stress |
Yield Stress (fy) | Depth of Neutral axis (xumax) |
250 | 0.53d |
415 | 0.48d |
500 | 0.46d |
Yield Stress (fy) | Moment of Resistance (Mulim) |
250 | 0.148 fckbd^{2} |
415 | 0.138 fckbd^{2 } |
500 | 0.133 fckbd2 |
Total value of Tensile force in steel
- T = 0.87 fy Ast
Total value of compressive force in concrete
- C = 0.36 fck b xu
LEVER ARM Calculation
Distance between total compression (C) and total tension (T).
- Lever arm = z = d – 0.42 xu
In case of SINGLY R.C. BEAM
- Moment of resistance is more over less.
- Ductility of beam is also less.
- It is not suitable for reversal of stresses.
DOUBLY R.C. BEAM
- Moment of resistance is more compared to singly reinforced beam.
- Ductility of beam is much more.
- It is Suitable for reversal of stresses.
Structural Component | Size of aggregate | Minimum clear Cover | Diameter of Re bar used in | ||||
Beam | 15 mm 20 mm | ||||||
Column | 12 mm | 40 mm | 12 mm | ||||
Slab | 15 mm | 20 mm | Main steel = 10 to 12 mm Distribution steel = 6 to 8 mm | ||||
Footing | 50 mm | ||||||
Equation for the width of flange of T-beam
Width = bf = l_{0}/6 + b_{w} + 6 D_{f}
DEVELOPMENT LENGTH
Length of reinforcement bar embedded in the concrete, which develop the value bond stress is called Development Length.
L_{d} = ∅ σs/4τbd
SHEAR REINFORCEMENT
Shear reinforcement is provided in the beam to resist the shear force & to keep the longitudinal bar in actual position bar binding.
Shear reinforcement is actually provided perpendicular way to the direction of the cracks.
Shear reinforcement is also may be provided whenever the τ > 0.5 N/mm2.
Section is redesigned if the τ > 2 N/mm2.
Shear Crack
When concrete strength is weak in tension, cracks are developed at 45° near support. These cracks are generally called Shear Crack.
Maximum spacing of Shear Reinforcement
0.75 d
300 mm
S_{v} = 0.87 f_{y}A_{sv}d/V_{us }
S_{v} = 0.87 f_{y}A_{sv}/0.4b
Equation for Nominal Shear Stress = τ_{u} = V_{u / }bd
- The maximum spacing of vertical reinforcement in case of R.C.C is equal to the 3 times of thickness of wall.
- Deformed bar is used in case of R.C.C to increase the bond within concrete medium.
- To minimum the eccentricity for column = e_{min} = l / 500+D / 30 = 20 mm
LATERAL TIE
The main purpose of use of lateral tie bar is to avoid the buckling of longitudinal bar.
Criteria for Pitch of lateral tie bar
- Least lateral dimension
- 16 x small diameter
- 300 mm, whichever is less.
Criteria for Diameter of lateral tie
- ¼ × Diameter of larger bar
- 6 mm, whichever is more.
Criteria for Column
- Minimum number of bars = 4 for Square column
= 6 for Circular column.
- Spacing of the bar along the periphery of column shall not exceed of 300 mm.
ONE WAY SLAB
- If l_{y}l_{x }≥ 2, then it’s considered as One-Way Slab.
- Main steel is provided along the direction of shorter side span.
- Distribution steel is provided along the direction of longer side span.
- Slab deflect along the shorter side of span.
TWO WAY SLAB
- If l_{y}l_{x} < 2, then it’s considered as Two-Way Slab.
- In both the direction, the Main steel is provided.
- Slab deflect along l_{x} and l_{y} both the direction.
CRITERIA FOR MAXIMUM SPACING OF BAR IN SLAB
For Main steel
3d
300 mm, whichever is smaller.
For Distribution steel
5d
450 mm, whichever is smaller.
EFFECTIVE SPAN FOR SIMPLY SUPPORTED SLAB/BEAM
Clear span + d
c/c of supports, whichever is smaller.
L / d RATIO FOR SLAB
For Cantilever beam l /d = 7.
For Simply supported beam l / d = 20.
For Continuous beam l / d = 26.
L / d RATIO FOR TWO WAY SLAB
For Mild Steel
- For Simply supported beam l / d = 35.
- For Continuous beam l / d = 40.
For HYSD bar, Value obtained from mild steel is multiplied by 0.8.
- In case of P.C.C, the maximum size of aggregate is 10 mm.
- In case of Column, Formwork is removed after 2 to 3 days.
- In case of Beam, Formwork is removed after 7 days.
- In case of Slab, Formwork is removed after 14 days.
- The deflection of the beam is limited to span/350 and 20 mm, whichever is less.
- The side face reinforcement is provided in R.C.C bean, if depth of web is exceeding 750 mm.
- Minimum grade of concrete required for
Pre-tensioned concrete = M 40
Post-tensioned concrete = M 30
Pre-stress concrete = M 30
As per loading type the load details are as follows
Part – I = Dead Load
Part – II = Live Load
Part – III = Wind Load
Part – IV = Snow Load
Part – V = Earthquake Load
% STEEL IN DIFFERENT STRUCTURE
Slab = Mild – 0.15%
HYSD – 0.12%
Beam = 0.34 to 4%
Shear wall = 0.25%
Water tank = 0.24%
Column = 0.8 to 6%
Bridge Slab = 0.30%
- Minimum thickness of flat slab = 125 mm.
- Thickness of shear wall not less than 150 mm.
DROP PANEL
Thickness of the slab is increased around the column is called Drop Panel.
Basically, Drop is provided to resist the shear forces.
- For R.C wall, Ratio of effective height to thickness = 30 limited.
- Maximum w/c ratio in R.C.C = 0.55.
CREEP COEFFICIENT
Loss of pre-stress in concrete = 12 to 20%.
Age | Creep coefficient |
7 days | 2.2 |
28 days | 1.6 |
1 year | 1 |
- In case of Design Mix, the Quantity of concrete ingredient in terms of Weight.
- In case of Nominal Mix, the Quantity of concrete ingredient in terms of Volume.
- If L / D = 2, then Deep Simply Supported Beam.
- If L / D = 2.5, then Deep Continuous Beam.
CRITERIA FOR LAP LENGTH
Development length
150 mm
Lap splice in beam not provided within
Joint
Distance of 2d from joint face
Within quarter length of the member.
Modular ratio (m) = 280/3σcb = Load carried by steel/Load carried by concrete
DESIGN OF R.C.C STRUCTURE
Three method is used for design
- Working Stress or Modular Ratio or Elastic Method
- Limit State or Plastic or Straight-Line Method
- Ultimate Strength or Load Factor Method
DIAGONAL TENSION
If the shear reinforcement is totally inadequate, the beam will fail in diagonal tension load application.
As per code provision Shear stress is less than 1/10 of the compressive stress in the concrete, then no shear reinforcement is required.
Diagonal tension
Diagonal tension is caused by the combined action of longitudinal tension and the transverse shearing stresses.
- The torsion Resisting Capacity of R.C section is actually increase with the decrease in stirrup spacing.
- Bond between the steel and concrete is mainly due to the pure adhesive resistance, frictional resistance & mechanical resistance properties.
- Spacing of the stirrups does not exceed the distance equal to the lever arm of the moment.
- The number of stirrups used is the ratio of lever arm to c/c spacing of stirrups.
- Stirrups: -It is shear reinforcement in the form of vertical re bars.
- c/c spacing of the stirrups in case of rectangular beam, is increased towards the centre and minimum near the supports ends.
If the bond stress is more than the permissible value then it written by
- Increasing the depth of beam
- Decreasing the diameter of the bars
- Increasing the number of bar.
OVERALL DEPTH OF T-BEAM
- For simply supported beam = 112 to 115 of span of beam.
- For continuous beam = 110 to 112 of span of beam.
- Effective depth for T-beam for light load = L20
DISTRIBUTION STEEL OR TRANSVERSE REINFORCEMENT
- Purpose of the distribution steel bar is to keep main the steel in actual position, distribute effect of the load uniformly and distribute shrinkage & temperature cracks evenly throughout the member.
- Distribution steel is provided at an angle of 90° to the span of the slab.
TWO WAY SLAB
- Slab simply supported on the four edges sides with corners not to held down, carrying the u.d.l analysed by Grashof and Rankine theory.
- Slab simply supported on the four edges with the corner held down, carrying the u.d.l analysed by, Marcus’s method & Pigeaud’s Method.
- Two-way slab can be analysed by the Pigand’s theory, Johnson’s theory & Westergaurd’s theory.
- Ribbed slab is provided where the Plain Ceiling, Thermal Insulation and Acoustic Insulation is required.
- Stair Rise = 150 mm to 200 mm
- Stair Tread = 250 mm to 300 mm
- Waist slab = 80 mm
- Tread + 2x Rise = 600 mm.
- Tread x Rise = 40,000 to 45,000 mm.
- Spread Footing: – It distribute load over a larger area.
- Simple Footing: – It provided for walls which carry light loads.
- Stepped Footing: – It provided for walls which carry heavy loads.
COMBINED FOOTING
- To support the two or more column which is near.
- To Provided when the bearing capacity is less.
- Strap Footing: – For two or more no of column, the load from the outer column is balanced by the inner column through cantilever beam acting about the fulcrum.
- Raft Footing: – It covers the entire area beneath a structure.
- Pile Foundation: – It is used where the top soil is relatively weak.
- End Bearing Pile: – It is used to transfer the loads through water or soft soil medium to a suitable bearing stratum.
- Friction Pile: – Used to transfer loads to a depth by means of skin friction along the length of the pile.
- Precast Concrete Pile: – Used for maximum design load of 80 tonnes except for large prestressed pile.
- Cast-in-situ Pile: – It is used in all ground condition.
- Pier Foundation: – It is suitable for heavy structure such as flyover.
- Well Foundation: -It is suitable for bridges.
- Minimum depth of footing by Rankine’s
D = PW 1−sinθ1+sinθ 2
- Shear crack in the pre-stressed concrete member depends upon the shape of the cross-section of the beam.
- Tensile strength = 10 to 15 % of Compressive strength.
RETAINING WALLS
- It is used to retain the earth fill or any other material so that the ground surfaces at different elevations level are maintained on either side of the retaining wall.
- It is used for roads in hilly areas, swimming pools, at the end of the bridges and underground water tanks or reservoirs.
Cantilever Retaining Wall
Utilising the weight of soil itself to provide the desired weight gain to counteract the load.
Gravity Retaining Wall
Depending on the own weight to provide the stability of the structure.
Counter fort Retaining Wall
- It is used the weight of the soil for stability.
- It provided when the height exceeding 6 m.
- The spacing of counter fort = 1/3 to 1/2 of height.
- The Factor of Safety due to the overturning in retaining wall is = 2.
- The Factor of Safety due to the sliding in retaining wall is = 1.5.
- Buttress in wall to provide the lateral support to wall.
- Basically shear key is provided if the retaining wall is not safe against the sliding.
- In case of toe slab of the retaining wall, reinforcement is provided at the bottom face.
- In stem portion of retaining wall, the reinforcement is provided near the earth side.
- In case of heel slab of the retaining wall, reinforcement is provided at top of the face.