| 28 CONCRETE CORBELS |
28.1 Design |
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1. Simplifying Assumptions: The concrete and reinforcement may be assumed to
act as elements of a simple strut-and-tie system, with the following guidelines: |
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a) The magnitude of the resistance provided to horizontal force should be not less than one- half of the design vertical load on the corbel.
b) Compatibility of strains between the strut-and-tie at the corbel root should be ensured.
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2. Reinforcement Anchorage: At the front face of the corbel, the reinforcement should be
anchored either by: |
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a) Welding to a transverse bar of equal strength- in this case of bearing area of the load should stop short of the face of the support by a distance equal to the cover of the tie reinforcement, or
b) Bending back the bars to form a loop- in this case of the bearing area of the load should not project beyond the straight portion of the bars of the forming the main tension reinforcement.
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3 Shear Reinforcement
Shear reinforcement should be provided in the form of horizontal links distributed in the upper two-third of the effective depth of the root of the corbel; this reinforcement should be not less than one-half of the area of the main tension reinforcement and should be adequately anchored.
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| 29. Deep Beam |
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29.1 Lever Arm
The lever arm ᵶ for a deep beam shall be determined as below:
For simply supported beams:
ᵶ=0.2 (l+2D) where 1≤ (l/D) ≤2
OR
ᵶ=0.6l Where (l/D) <1
For continuous beams:
ᵶ=0.2(l+1.5D) Where 1≤ (l/D) ≤2.5
OR
ᵶ=0.5l Where (l/D) < 1
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Where,
l -- the effective span taken as centre to centre distance between supports or 1.15 times the clear span whichever is smaller, and D is the overall depth. |
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29.2 Reinforcement
1. Positive Reinforcement
The tensile reinforcement required to resist positive bending moment in any span of a beam shall:
→ Extend without curtailment between supports.
→ Be embedded beyond the face of each support, so that the face of the support it shall have a development length not less than 0.8Ld
Ld→development length
→ Be placed with in a zone of depth equal to 0.25D-0.05l adjacent to the tension face of the beam.
Where, D- overall depth; l= effective span
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2 Negative Reinforcement
a) Termination of reinforcement- For tensile reinforcement required to resist negative bending moment over a support of a deep beam
1) It shall be permissible to terminate not more than half of the reinforcement at a distance of 0.5D from the face of the support where D is as defined in 29.2 ; and
2) The remainder shall extend over the full span.
b) Distribution- When ratio of clear span to overall depth is in the range 1.0 to 2.5, tensile reinforcement over a support of a deep beam shall be placed in two zones comprising:
1) A zone of depth 0.2D, adjacent to the tension face, which shall contain a proportion of the tension steel given by:
0.5(l/D-0.5)
Where
l=clear span,and
D=overall depth
2) A zone measuring 0.3 D on either side of the mid-depth of the beam which shall contain the remainder of the tension steel, evenly distributed.
For span to depth ratios less than unity, the steel shall be evenly distributed over a depth of 0.8 D measured from the tension face.
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3. Vertical Reinforcement
If forces are applied to a deep beam in such a way that hanging action is required, bars or suspension stirrups shall be provided to carry all the forces concerned.
4. Side Face Reinforcement
Side face reinforcement shall comply with requirements of minimum reinforcement of walls (see32.4)
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| 30 RIBBED, HOLLOW BLOCK OR VOIDED SLAB |
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30.1 General
This covers the slabs constructed in one of the ways described below:
a) As a series of concrete ribs with topping cast on forms which may be removed after the concrete has set;
b) As a series of concrete ribs between precast blocks which remain part of the completed structure; the top of the ribs may be connected by a topping of concrete of the same strength as that used in the ribs; and
c) With a continuous top and bottom face but containing voids of rectangular, oval or other shape.
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30.2 Shear
Where hollow blocks are used, for the purpose of calculating shear stress, the rib width may be increased to take account of the wall thickness of the block on one side of the rib; with narrow precast units, the width of the jointing mortar or concrete may be included.
30.3 Deflection
The recommendations for deflection in respect of solid slabs may be applied to ribbed, hallow block or voided construction. The span to effective depth ratios given in 23.2 for a flanged beam are applicable but when calculating the final reduction factor for web width, the rib width for hallow block slabs may be assumed to include the walls of the blocks on both sides of the rib. For voided slabs and slabs constructed of the box or I- section units, an effective rib width shall be calculated assuming all material below the upper flange of the unit to be concentrated in a rectangular rib having the same cross-sectional area and depth.
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30.4 Size and Position of Ribs
In-situ ribs shall not be less than 65mm wide. They shall be spaced at centres not greater than 1.5m apart and their depth, excluding any topping shall be not more than four times their width. Generally ribs shall be formed along each edge parallel to the span of one way slabs.
30.5 Hollow Blocks and formers- IS 3951 ( Part-1)
When required to contribute to the structural strength of the slab they shall:
a) Be made of concrete or burnt clay; and
b) Have a crushing strength of at least 14-N/mm2 measured on the net section when axially loaded in the direction of compressive stress in the slab
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30.6 Arrangement of Reinforcement
The recommendations given in 26.3 regarding maximum distance between bars apply to areas of solid concrete and cover to reinforcement shall be as described below:
a) At least 50 percent of the total main reinforcement shall be carried through at the bottom on to the bearing and anchored in accordance with 26.2.3.3
b) Where slab, which is continuous over supports, has been designed as simply supported, reinforcement shall be provided over the support to control cracking. This reinforcement shall have a cross-sectional area of not less than one- quarter that required in the middle of the adjoining spans and shall extend at least one-tenth of the clear span into adjoining spans.
c) In slabs with permanent blocks, the side cover to the reinforcement shall not be less than 10mm. In all other cases, cover shall be provided according to 26.4
30.7 Precasts Joists and Hollow Filler Blocks
The construction with precast joists and hollow concrete filler blocks shall conform to IS 6061 (Part 1) and precast joist and hollow clay filler blocks shall conform to IS 6061 (part 2)
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| 31. Flat slabs |
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The term flat slab means a reinforced concrete slab with or without drops, supported
generally without beams, by columns with or without flared column head ( see fig. 12) |
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31.1 The following definitions shall apply:
a) Column strip- Column strip means a design strip having a width of 0.25l2 , but not greater than 0.25 l2 on each side of the column centre line, where l1 is the span in the direction moments are being determined, measured entre to centre of supports
l2 is the span transverse to l1 , measured centre to centre of supports
b)Middle Strip- Middle strip means a design strip bounded on each side of its opposite side by the column strip
c) Panel- Panel means that part of a slab bounded on each of its four sides by the centre line of a column or centre- lines of adjacent spans.
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31.2 Proportioning
1. Thickness of flat slab
For slabs with drops conforming to next point, span to effective depth varies given in 23.2 shall be applied directly, otherwise the span to effective- depth ratio obtained in accordance with provisions in 23.2 shall be multiplied by 0.9 for this purpose, the longer span shall be considered, the minimum thickness of slab shall be 125mm.
2 Drop
The drops when provided shall be rectangular in plan, and have a length in each direction not less than one- third of the panel length in that direction. For exterior panels, the width of drops at right angles to the non- continuous edge and measured form the centre-line of the columns shall be equal to one-half the width of drop for exterior panels.
3 Column Heads
Where column heads are provided, that portion of a column head which lies within the largest right circular cone or pyramid that has a vertex angle of 90° and can be included entirely within the outlines of the columns and the columns head, shall be considered for design purposes (see fig.12)
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31.3 Determination of Bending Moment
1. Bending moments in panels with Marginal Beams or walls
Where the slab is supported by a marginal beam with a depth greater than 1.5 times the thickness of the slab or by a wall, then:
a) The total load to be carried by the beam or wall shall comprise those loads directly on the wall or beam plus a uniformly distributed load equal to one- quarter of the total load on the slab, and
b) The bending moments on the half- column strip adjacent to the beam or wall shall be one- quarter of the bending moments for the first interior column strip.
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2. Transfer of Bending Moments to Columns
When unbalanced gravity load, wind, earthquake, or other lateral loads cause transfer of bending moment between slab and column, the flexural stresses shall be investigated using a fraction, α of the moment given by:
α=1/(1+2/3 √(a1⁄a2 ))
Where,
a1= Overall dimensions of the critical section for shear in the direction in which moments acts and
a2= Overall dimensions of the critical section for shear transverse to the direction in which moment acts.
A slab width between lines that are one and one- half slab or drop panel thickness; 1.5D, on each side of the column or capacity may be considered effective, D being the size of the column.
Concentration of reinforcement over column head by closer spacing or additional reinforcement may be used to resist the moment on this section.
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31.4 Direct Design Method
1. Limitations
Slab system designed by the direct design method shall fulfil the following conditions
a) There shall be minimum of three continuous spans in each direction,
b) The panels shall be rectangular, and the ratio of the longer span to the shorter span within a panel shall not be greater than 2.0,
c) It shall be permissible to offset columns to a maximum of 10 percent of the span in the direction of the offset notwithstanding the provision in (b)
d) The successive span lengths in each direction shall not differ by more than one-their of the longer span. The end spans may be shorter but longer than the interior spans, and
e) The design live load shall not exceed three times the design dead load.
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2. Total Design Moment for a Span
→ In the direct design method, the total design moment for a span shall be determined for a strip bounded laterally by the centre- line of the panel on each side of the centre- line of the supports.
→ The absolute sum of the positive and average negative bending moments in each directions shall be taken as:
Mo=(Wln)/8
Where
Mo=total moment;
W= design load on an area l2 ln
ln = clear span extending from face to face of columns, capitals, brackets or walls bur not less than 0.65l_(1;)
l1= length of span in the direction of Mo; and
l2= length of span transverse to l1
→ Circular supports shall be treated as square supports having the same area.
→ When the transverse span of the panels on either side of the centre-line of supports varies, l2 shall be taken as the average of the transverse spans
→ When the span adjacent and parallel to an-edge is being considered, the distance from the edge to the centre- line of the panel shall be substituted for l2 in Mo.
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3. Negative and Positive Design Moments
a) The negative design moment shall be located at the face of rectangular supports, circular supports being treated as square supports having same area.
b) In an interior span, the total design moment Mo shall be distributed in the following proportions:
Negative design moment 0.65
Positive design moment 0.35
c) In an end span, the total design moment Mo shall be distributed in the following proportions:
Interior negative design moment:
0.75-0.10/(1+1/αc )
Positive design moment:
0.63-0.28/(1+αc )
Exterior negative design moment
0.65/(1+1/αc )
αc is the ratio of flexural stiffness of the exterior columns to the flexural stiffness of the slab at a joint taken in the direction moments are being determined and is given by
αc = (σKc)/K'
Where
Kc= Sum of the flexural stiffness of the columns meeting at the joint; and
K'= Flexural stiffness of the slab, expressed as moment per, unit rotation.
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d)Moments in Columns
→Columns built integrally with the slab system shall be designed to resist moments arising from loads on the slabs system.
→At an interior support, the supporting members above and below the slab shall be designed to resist the moment M given by the following equation, in direct proportion to their stiffness unless a general analysis is made:
M =0.08 ((wd+0.5w₁ ) l₂ l₁ᶟ-w′d l'₂ l′₁²)/(1+1/αc )
Where
wd, w₁=design dead and live loads respectively,per unit area;
l₂=length of span tranverse to the direction of M
ln=length of the clear span in the direction of M,measured face to face of supports
αc = (σKc)/(σK' )
where
wd' l′₂ and l₁′² refer to the shorter span.
e) Effects of pattern Loading
In the direct design method, when the ratio of live load to dead exceed 0.5:
The sum of the flexural stiffness of the columns above and below the slab, σ K_c, shall be much that α_c is not less than appropriate minimum value α_cminspecified in Table 17 or
If the sum of the flexural stiffness’s of the column σ K_c, does not satisfy (a), the positive design moments for the panel shall be multiplied by the coefficient β_s given by the following equation
βs=1+((2-wd/w₁ )/(4+wd/w₁ ))(1-a_c/a_cmin )
α_c is the ratio of flexural stiffness of the columns above and below the slab to the flexural stiffness of the slabs at a joint taken in the direction moments are being determined and is given by:
a_c= σ K_c,/σ K_s,
K_c, and σK_s, are flexural stiffness of column and slab respectively
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Table 17 Minimum Permissible value of α_c
(Clause 31.4.6)
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Imposed Load/ Dead Load |
Ratio |
Value of |
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-1 |
-2 |
-3 |
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0.5 |
0.5 to 2.0 |
0 |
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1 |
0.5 |
0.6 |
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1 |
0.8 |
0.7 |
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1 |
1 |
0.7 |
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1 |
1.25 |
0.8 |
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1 |
2 |
1.2 |
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2 |
0.5 |
1.3 |
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2 |
0.8 |
1.5 |
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2 |
1 |
1.6 |
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2 |
1.25 |
1.9 |
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2 |
2 |
4.9 |
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3 |
0.5 |
1.8 |
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3 |
0.8 |
2 |
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3 |
1 |
2.3 |
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3 |
1.25 |
2.8 |
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3 |
2 |
13.8 |
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31.6 Shear in Flat Slab
1. The critical section for shear shall be at a distance d/2 from the periphery of the column/capital/drop panel, perpendicular to the plane of the slab where d is the effective depth of the section (see fig 12)
The shape in plan in geometrically similar to the support immediately below the slab (see Fig 13.A and 13B)
Note- For column sections with re- entrant angles, the critical section shall be taken as indicated in Fig. 13C and 13D
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→ In the case of columns near the free edge of a slab, the critical section shall be taken as shown in Fig.14
→ When openings in flat slabs are located at a distance less than ten tomes the thickness of the slab from a concentrated reaction or when the openings are located within the column strips, the critical sections specified in pint (1) shall be modified so that the part of the periphery of the critical section which is enclosed by radial projections of the openings to the centroid of the reaction area shall be considered ineffective (see fig 15) and the openings shall not encroach upon column head.
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2 Calculation of Shear Stress
a)The nominal shear stress in flat slabs shall be taken as V/b_0 d where V is the shear force due to design load, b_0 is the periphery of the critical section and d is the effective depth.
b) When unbalanced gravity load, wind, earthquake or other forces cause transfer of bending moment between slab and column, a fraction (1- α) of the moment shall be considered transferred by eccentricity of the shear about the centroid of the critical section. Shear stresses shall be taken as varying linearly about the centroid of the critical section. The value of α shall be obtained from the equation given in 31.3 |
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3 Permissible Shear stress
→When shear reinforcement is not provided the calculated shear stress at the critical section shall not exceed Kв τс
Where
Kв=(0.5+βc ) but not greater than 1,βc being the ratio of short side to long side of the column/capital; and
τс=0.25√fck in limit state method of design,
And 0.16 √fck in working stress method of design.
→When the shear at the critical section exceeds the value given above, but less than 1.5τ_c shear reinforcement shall be provided. If the shear stress exceeds1.5τc, the flat slab shall be redesigned. Shear stresses shall be investigated t successive sections more distant from the support and shear reinforcement shall be provided up to a section where the shear stress does not exceed 0.5τc. While designing the shear reinforcement, the shear stress carried by the concrete shall be assumed to be 0.5τc and reinforcement shall carry the remaining shear.
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31.7 Slab Reinforcement
1 Spacing
The spacing of bars in a flat slab shall not exceed 2 times the slab thickness, except where a slab is of cellular or ribbed contribution.
2 Area of Reinforcement
When drop panels are used, the thickness of drop panel for determination of area reinforcement shall be the lesser of the following:
a) Thickness of drop, and
b) Thickness of slab plus one quarter the distance between edge of drop and edge of capital.
3 Minimum Length of Reinforcement
a) Reinforcement in flat slabs shall have the minimum lengths specified in fig.16. Larger lengths of reinforcement shall be provided when required by analysis
b) Where adjacent spans are unequal, the extensions of negative reinforcement beyond each face of the common shall ve based on the longer span.
c) The length of reinforcement for slabs frames not braced against sideways and for slabs resisting lateral loads shall be determined by analysis but shall not be less than those prescribed in fig.16
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Fig. 16 Minimum Bend Joint Location and Extensions for Reinforcement by Flat Slabs |
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Bar length from face of Support |
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Minimum length |
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Maximum length |
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Mark |
A |
b |
c |
d |
e |
f |
g |
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Length |
0.14l |
0.20l |
0.22l |
0.30l |
0.33l |
0.20l |
0.24l |
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• Bent bars at exterior supports may be used if a general analysis is made
Note- D is the diameter of the column and the direction dimensions of the rectangular column in the direction under consideration.
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4 Anchoring Reinforcement
a) All slabs reinforcement perpendicular to a discontinuous edge shall have an anchorage (straight, bent or otherwise anchored) past the internal face of the spandrel beam, wall or column, of an amount:
1. For positive reinforcement- not less than 150mm except that with fabric reinforcement having a fully welded transverse wire directly over the support, it shall be permissible to reduce this length to one- half of the width of the support or 50mm whichever is greater
2. For negative reinforcement- such that the design stress is developed at the internal face, on accordance with section 3.
b) Where the slab is not supported by a spandrel beam or wall, or where the slab cantilever beyond the support, the anchorage shall be obtained within the slab.
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| 32. WALLS |
32.1 Empirical Design Method for
Walls Subjected to Inplane Vertical Load |
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The minimum thickness of walls shall be 100 mm.
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1 Braced Walls
Walls shall be assumed to be braced if they are laterally supported by a structure in which all the following apply:
a) Walls or vertical braced elements are arranged in two directions so as to provide lateral stability to the structure as a whole
b) Lateral forces are resisted by shear in the planes of these walls or by braced elements
c) Floor and roof systems are designed to transfer lateral forces
d) Connections between the wall and the lateral supports are designed to resist a horizontal force not less than
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1) The simple static reactions to the total applied horizontal forces at the levels of lateral support; and
2) 2.5 percent of the total vertical load that the wall is designed to carry at the level of lateral support
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2 Eccentricity of Vertical Load
The design of a wall shall take account of the actual eccentricity of the vertical force subject to a minimum value of 0.05t.
The vertical load transmitted to a wall by a discontinuous concrete floor or roof shall be assumed to act at one-third the depth of the bearing area measured from the span face of the wall. Where there is-situ concrete floor continuous over the wall, the load shall be assumed to act at the centre of the wall.
The resultant eccentricity of the total vertical load on a braced wall at any level between horizontal lateral supports, shall be calculated on the assumption that the resultant eccentricity of all the vertical loads above the upper support is zero.
3 Maximum Effective Height To Thickness Ratio
The ratio of effective height to thickness, HWC lt shall not exceed 30
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4 Effective Height
The effective height of a braced wall shall be taken as follows:
a) Where restrained against rotation at both ends by IS 456:2000
1) Floors 0.75Hw or
2) Intersecting walls or similar members whichever is the lesser 0.75L₁
b) Where not against rotation at both ends by
1) Floors 1.0Hw or
2) Intersecting walls or similar members whichever is lesser 1.0L₁
Where,
Hw = the unsupported height of the wall.
L₁ = the horizontal distance between centres of lateral resistant
5 Design Axial Strength of Wall.
The design axial strength P_uw per unit length of braced wall in compression may be calculated from the following equation:
P_uw = 0.3 (t-1.2e-2eₐ)f_ck
Where
t=thickness of wall
e=eccentricity of load at right angles to the plane of the wall
eₐ=additional eccenrtricity due to slenderness effect taken as H_we/500t.
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32.2 walls subjected to Cobined
Horizontal and Vertical Forces |
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Walls subjected to horizontal forces perpendicular to the wall and for which the design axial load
does not exceed 0.04 f_ck A_K shall be designed as slabs in accordance with appropriate provisions under 24, where A_g is gross area of the section. |
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1. Design for Horizontal Shear |
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1. Critical Section for Shear
The critical section for maximum shear shall be taken at a distance from the base of 0.5 L_w or 0.5H_w whichever is less
2. Nominal Shear Stress
The nominal shear stress τ_vw in walls shall be obtained
τ_vw = V_u/t.d
Where
V_u=shear force due to design loads
t=wall thickness
d=0.8×L_w is the length of the wall
Under no circumstances shall the nominal shear stress τ_vw in wall exceed 0.17f_ck in limit state method and 0.12 f_ck in working stress method.
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3 Design Shear Strength of Concrete
The design shear strength of concrete in walls, τ_cw, without shear reinforcement shall be taken as below
a) For H_w/L_w ≤ 1
τ_cw=(3.0-H_w/L_w) K₁ √(f_ck )
Where K₁ is 0.2 in limit state method and 0.13 in working stress method.
b) For H_w/L_w>1
Lesser of the values calculated from (a) above and from
τ_cw = K₂ √(f_ck ) * ((H_w/L_w+1))/((H_w/L_w-1))
Where K₂ is 0.045 in limit state method and 0.03 in working stress method, but shall be not less than K₃ √(f_ck ) in any case where K₃ is 0.15 in limit state method and 0.10 in working stress method
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4 Design of Shear Reinforcement
Shear Reinforcement shall be provided to carry a shear equal to V_u- τ_cw.t (0.8L_w). In case of working stress method V_u is replaced by V. The strength of shear reinforcement shall be calculated as per 40.4 or B-5.4 with A_av defined as below
A_av= P_w (0.8L_w )t
Where P_w=is determined as follow
For walls where H_w/L_w≤1,P_w shall be the lesser of the ratios of either the vertical reinforcement area or the horizontal reinforcement area to the ross-sectional area of wall in the respective direction.
For walls where H_w/L_w >1,P_w shall be the ratio of the horizontal reinforcement area to the cross-sectional area of wall per vertical metre.
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5 Minimum Requirements for Reinforcement in Walls
The reinforcement for walls shall be provided as below:
a) The minimum ratio of vertical reinforcement to gross concrete area shall be :
1) 0.001 2 for deformed bars not larger than 16mm in diameter and with a characteristics strength of 415N/mm2 or greater.
2) 0.001 5 for other types of bars
3) 0.0012 for welded wire fabric not larger than 16mm in diameter.
b) Vertical reinforcement shall be spaced out farther apart than three times the wall thickness nor 450mm.
c) The minimum ratio of horizontal reinforcement to gross concrete area shall be:
1) 0.002 0 for deformed bars not larger than 16mm in diameter and with a characteristics strength of 415N/mm2 or greater
2) 0.002 5 for other types of bars
3) 0.002 0 for welded wire fabric not larger than 16mm in diameter
d) Horizontal reinforcement shall be spaced not farther apart than three times the wall thickness nor 450mm.
NOTE- The minimum reinforcement may not always be sufficient to provide adequate resistance to the effects of shrinkage and temperature.
→ For walls having thickness more than 200mm, the vertical and horizontal reinforcement shall be provided in two grids, one near each face of the wall.
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| 33. STAIRS |
33.1 Effective Span of Stairs |
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The effective span of stairs without stringer beams shall be taken as the following horizontal distances:
a) Where supported at top and bottom risers by beams spanning parallel with the risers, the distance centre-to centre of beams
b) Where spanning on the edge of landing slab, which spans parallel, with the risers ( see fig. 17) a distance equal to the going of the stairs plus at each end either half the width of the landing or one metre, whichever is smaller; and
c) Where the landing slab spans in the same direction as the stairs, they shall be considered as acting together to form a single slab and the span determined as the distance centre-to-centre of the supporting beams or walls, the going being measured horizontally. |
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33.2 Distribution of Loading on Stairs |
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In the case of stairs with open wells, where spans partly crossing at right angles occur, the load on
areas common to any two such spans may be taken as one-half in each direction as shown in fig. 18. Where flights or landings are embedded into walls for a length of not less than 110mm and are designed to span in the direction of the flight, a 150mm strip may be deducted from the loaded area and the effective breadth of the section increased by 75mmnfor purpose of design (see fig 19) |
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Fig.19 Loading on stairs built into walls |
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33.3 Depth of section |
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The depth of section shall be taken as the minimum thickness perpendicular to the soffit of the staircase. |
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| 34. FOOTINGS |
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Thickness at the Edge of Footing
In reinforced and plane concrete footing, the thickness at the edge shall be not less than 150mm for footings on soils, nor less than 300mm above the tops of piles for footings on piles.
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In the case of plain concrete pedestals, the angles between the planes passing through the bottom edge of the pedestal and the corresponding junction edge of the column with pedestal and the horizontal plane (see fig.20) shall be governed by the expression:
tan a≮0.9√((100q₀)/f_ck )
Where
q₀=calculated maximum bearing pressure at the base of the pedestal in N/mm², and
f_ck=characteristics strength of concrete at 28 days in N/mm²
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34.1 Moments and Forces |
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1. Shear and Bond
The shear strength of footings is governed by the more severe of the following two conditions:
a) The footing acting essentially as a wide beam, with a potential diagonal crack extending in a plane across the entire width; the critical section for this condition shall be assumed as a vertical section located from the face of the column, pedestal or wall at a distance equal to the effective depth of footing for footings on piles.
b) Two-way action of the footing, with potential diagonal cracking along the surface of truncated cone or pyramid around the concentrated load; in this case, the footing shall be designed for shear in accordance with appropriate provisions specified in 31.6
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In computing the external shear or any section through a footing supported on piles, the entire reaction
from any pile of diameter D_p whose centre is located D_p/2 or more outside the section shall be assumed as producing shear on the section; the reaction from any pile whose centre is located D_p/2 or more inside the section shall be assumed as producing nor shear on the section. For intermediate positions of the pile centre, the portion of the pile reaction to be assumed as producing shear on the section shall be on straight line interpolation between full value at D_p/2 outside the section and zero value atD_p/2 inside the section. |
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2. Tensile Reinforcement
Total tensile reinforcement shall be distributed across the corresponding resisting section as given below:
a) In one- way reinforced footing, the reinforcement extending in each direction shall be distributed uniformly across the full width of the footing;
b) In two- way reinforced square footing, the reinforcement extending in each direction shall be distributed uniformly across the full width of the footing; and
c) In two-way reinforced rectangular footing, the reinforcement in long direction shall be distributed uniformly across the full width of the footing. For reinforcement in the short direction, a central band equal to the width of the footing shall be marked along the length of the footing portion of the reinforcement determined in accordance with the equation given below shall be uniformly distributed across the central band:
(Reinforcement in central band width)/(Total reinforcement in short direction)=2/(β+1)
Where:
β is the ratio of the long side to the short side of the footing. The remainder of the reinforcement shall be uniformly distributed in the outer portion of footing.
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3. Transfer of Load at the Base of Column
The compressive stress in concrete at the base of a column or pedestal shall be considered as being transferred by bearing to the top of the supporting pedestal or footing. The bearing pressure on the loaded area shall not exceed the permissible bearing stress in direct compression multiplied by a value equal to
√(A₁/A₂ ) but not greater than 2;
Where
A₁= Supporting area for bearing of footing, which is sloped or stepped footing may be taken as the area of the lower base of the largest frustum of a pyramid or cone contained wholly within the footing and having for its upper base, the area actually loaded and having side slope of the vertical to two horizontal; and
A₂= Loaded area at the column base.
For working stress method of design the permissible bearing stress on full area of concrete shall be taken as 0.25f_ck; for limit state method of design the permissible bearing stress shall be 0.45f_ck.
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4. Nominal Reinforcement
→ Minimum reinforcement and spacing shall be as per the requirements of solid slab.
→ The nominal reinforcement for concrete sections of thickness greater than 1m shall be 360mm2 per metre length in each direction on each face. This provision does not supersede the requirement of minimum tensile reinforcement based on the depth of the section.
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| 35. Limit State Method |
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In the method of design based on limit state concept, the structure shall be designed to withstand safely all loads liable to act on it throughout its life, it shall also satisfy the serviceability requirements, such as limitations on deflection and cracking.
The design should be based on characteristics values for material strengths and applied loads. The characteristics values should be based on statistical data if available, where such data, are not available they should be based on experience. |
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35.1 Limit State of Collapse
The limit state of collapse of the structure or part of the structure could be assessed from rupture of one or more critical sections and from buckling due to elastic or plastic instability (including the effects of sway where appropriate) or overturning. The resistance to bending, shear, torsion and axial loads at every section shall not be less than the appropriate value at that section produced by the probable most unfavourable combinations of loads on the structure using the appropriate partial safety factors.
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35.2 Limit States of Serviceability |
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1. Deflection
Clause 23.2
2. Cracking
Crack width calculating may be done using formula given in Annex F.
The surface width of the cracks should not in general, exceed 0.3mm in members where cracking is not harmful and does not have any serious adverse effects upon the preservation of reinforcing steel nor upon the durability of the structures. In members where cracking in the tensile zone is harmful either because they are exposed to the effects of the weather or continuously exposed to moisture or in contact soil or ground water, an upper limit of 0.2mm is suggested for the maximum width of cracks. For particularly aggressive environment, Such as the ‘ Severe’ category in Table 3, the assessed surface width of cracks should not in general exceed 0.1mm.
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| 36 Characteristics AND Design Values
and Partial Safety Factors- |
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36.1 Characteristics Strength of Materials
The term ‘characteristics strength’ means that value of strength of the material below which not more than 5% of the test results are expected to fall. The characteristics strength for concrete shall be in accordance with table 2.
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36.2 Characteristics Loads
The term ‘characteristics Load’ means that value of load which as 95% probability of not being exceeded during the life of a structure.
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36.3 Design Values |
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1. Materials
The design strength of the materials, f_d is given by
f_d=f/γ_m
Where
f=characteristics strength of the material (see 36.1)and
γ_m=partial safety factor appropriate to the material and
the limit state being considered
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2. Loads
The design load, F_d is given by
F_d=F γ_f
Where
F= Characteristics load (see 36.2) and
γ_f= Partial safety factor appropriate to the nature of loading and the limit state of being considered.
3. Consequences of Attaining Limit State
Where the consequences of a structure attaining a limit state are of a serious nature such as huge loss of life and disruption of the economy, higher values for γ_f and γ_mthan those given under 36.4.1 and 36.4.2 may be applied.
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36.4 Partial Safety Factors |
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1. Partial Safety Factor γ_f for loads
The values of γ_f given in Table 18 shall normally be used.
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Table 18 Values of Partial Safety Factor γ_f for loads
(Clause 18.2.3.1, to 36.4.1 and B-4.3) |
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Load Combination |
1.5 or - 1.5 |
Limit States of serviceability |
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-1 |
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DL IL WL |
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DL+IL |
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(5) (6) (7) |
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DL+WL |
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1.0 1.0 - |
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1.0 - 1.0 |
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DL+IL+WL |
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1.0 0.8 0.8 |
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NOTES:
1. While considering earthquake effects, substitute EL for WL
2.For the limit states of serviceability, the value of γ_fgiven in this table are applicable for short term effects. While assessing the long term effects due to creep the dead load and that part of the live load likely to be permanent may only be considered
3.The value is to be obtained when stability against overturning or stress reversal is critical
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2. Partial Safety factor γ_m for Material Strength
→ When assessing the strength of a structure or structural member for the limit state of collapse, the values of partial safety factor, γ_m should be taken as 1.5 for concrete and 1.15 for steel.
Note- γ_m values are already incorporated in the equations and the tables given in this standard for limit state design.
→When assessing the deflection, the material properties such as modulus of elasticity should be taken as those associated within the characteristics strength of the material. |
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| 37. ANANLYSIS |
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1. Redistribution of Moments in Continuous Beams and Frames
The redistribution of moments may be carried out satisfying the following conditions:
a) Equilibrium between the internal forces and the external loads is maintained
b)The ultimate moment of resistance provided at any section of a member is not less than 70 percent of the moment at that section obtained from an elastic maximum moment diagram covering all appropriate combinations of loads.
c)The elastic moment at any section in a member due to a particular combination of loads shall not be reduced by more than 30 percent of the numerically largest moment given anywhere by the elastic maximum moments diagram for the particular members, covering all appropriate combination of loads
d)At sections where the moment capacity after redistribution is less than that from the elastic maximum moment diagram, the following relationship shall be satisfied:
x_u/d+δM/100 ≤ 0.6
Where
x_u=depth of neutral axis,
d=effective depth and
δM=percentage reduction in moment
e) In structure in which in structural frame provides the lateral stability, the reduction in moment allowed by condition 37.1.1 (c) shall be restricted to 10 percent for structures over 4 stores in g=height.
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2. Analysis of Slabs Spanning in Two Directions at Right Angles
Annex D
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| 38. Limit State of Collapse : Flexure |
38.1 Assumptions |
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Design for the limit state of collapse in flexure shall be based on the assumptions given below:
a)Plane sections normal to the axis remains plane after bending
b)The maximum strain in concrete at the outermost compression fibre is taken as 0.0035 in bending.
c)The relationship between the compressive stress distribution in concrete and the strain in concrete may be assumed to be rectangular, trapezoid, parabola or any other shape which results in prediction of strength in substantial agreement with the results of test. An acceptable stress-strain curve is given in fig.21. for design purposes, the compressive strength of concrete in the structure shall be assumed to be 0.67 times the characteristics strength. The partial safety factor γ_m=1.5 shall be applied in addition to this.
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Note- for the stress-strain curve in Fig .21 the design stress block parameters are as follows (see fig 22)
Area of Stress block = 0.36f_ck.X_u
Depth of the centre of compressive force from the extreme fibre in compression = 0.42X_u
Where
f_ck.=characteristics compressive strength of concrete and
X_u= depth of neutral axis
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Fig. 22 STRESS BLOCK PARAMETERS |
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d)The tensile strength of concrete is ignored
e)The stresses in the reinforcement are derived from the representative stress-strain curve for the type of steel used. Typical curves are given in Fig.23 for design purposes the partial safety factor γ_m, equal to 1.15 shall be applied.
f)The maximum strain in the tension reinforcement in the section at failure shall not be less than:
f_y/(1.15E_s )+0.002
Where
f_y=characteristics strength of steel,and
E_s=modulus of elasticity
NOTE- The limiting values of depth of neutral axis for different grades of steel base on the assumptions in 38.1 are as follows:
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250 |
0.53 |
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415 |
0.48 |
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500 |
0.46 |
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The expression for obtaining the moments of resistance for rectangular and T-sections, based on the
assumptions of 38.1 are given in Annex G |
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| 39. Limit State of Collapse: Combination |
39.1 Assumptions |
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In addition to the assumptions given in 38.1 (a) to (e) for flexure, the following shall be assumed:
38.1 (e) for flexure, the following shall be assumed:
a) The maximum compressive strain in concrete in axial compression is taken as 0.002
b) The maximum compressive strain at the highly compressed extreme fibre in concrete subjected to axial compression and bending and when there is no tension on the section shall be 0.0035 minus 0.75 times the strain at the least compressed extreme fibre.
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39.2 Minimum Eccentricity |
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All members in compression shall be designed for the minimum eccentricity in the accordance with 25.4. Where calculated eccentricity is larger, the minimum eccentricity should be ignored. |
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39.3 Short Axially Loaded Members in
Compression |
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The member shall be designed by considering the assumptions given in 39.1 and the minimum eccentricity. When the minimum eccentricity as per 25.4 does not exceed 0.05 times the lateral dimensions, the members may be designed by the following equations:
P_s= 0.4f_ck.A_c + 0.67f_y.A_ac
Where
P_s= Axial load on the member,
f_ck.= characteristic compressive strength of the concrete
A_c= Area of concrete,
f_y = characteristics Strength of the compression reinforcement, and
A_ac= Area of longitudinal reinforcement for columns.
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39.4 Compression Members with
Helical Reinforcement |
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The strength of compression members with helical reinforcement satisfying the requirement of 39.4.1 shall be taken as 1.05 times the strength of similar member with lateral ties.
→ The ratio of the volume of helical reinforcement to the volume of the core shall not be less than 0.36 (A_s/A_c-1) f_ck/f_y
Where
A_s= Gross area of the section
A_c= Area of the core of the helically reinforced column measured to the outside diameter of the helix
f_ck= Characteristics compressive strength of the concrete, and
f_y= Characteristics strength of helical reinforcement but nit exceeding 415N/mm2
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39.5 Members Subjected to Combined Axial Load and Uniaxial Bending
All members subjected to axial force and uniaxial bending shall be designed on the basis of 39.1 and 39.2
NOTE- The design of member subject to combined axial load and uniaxial bending will involve lengthy calculation by trial and error. In order to overcome these difficulties interaction diagrams may be used. These have been prepared and published by BIS on ‘SP :16 Design aids for reinforced concrete IS 456’
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39.6 Members subjected to Combined Axial Load and Biaxial Bending
The resistance of a member subjected to axial force and biaxial bending shall be obtained on the basis of assumptions given in 39.1 and 39.2 with neutral axis so chosen as to satisfy the equilibrium of load and moments about two axes. Alternatively such members may be designed by the following equations:
[M_ux/M_ux1 ]^(a_s )+[M_uy/M_uy1 ]^(a_s )≤1.0
Where
M_ux M_uy = moments about x and y axes due to design loads.
M_ux1 M_uy1 = maximum uniaxial moment capacity for an axial load of P_u, bending about x and y axes respectively, and
a_s is related to P_u/P_ux
Where
P_ux = 0.45f_(ck.) A_c+0.75f_y.A_ac
For values of P_u/P_ux = 0.2 to 0.8, the value of a_s vary linearly from 1.0 to 2.0.For values less than 0.2a_s is 1.0 for values greater than 0.8a_s is 2.0
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39.7 Slenderness Compression Members
The design of slender compression members (see 25.1.1) shall be based on the forces and the moments determined from an analysis of the structures including the effect of deflections on moments and forces. When the effect of deflections are not taken into account in the analysis, additional moment given in 39.7.1 shall be taken into account in the appropriate direction.
→ The additional moments M_ax and M_ay shall be calculated by the following formulae:
M_ax= (P_u D)/2000{l_ax/D }^(2 )
M_ay =(P_u b)/2000{l_ay/b }^(2 )
Where
P_u = axial load on the member
l_ax=effective length in respect of the major axis
l_ay=effective length in respect of the minor axis
D= Depth of the cross-section at right angles to the major axis, and
b=width of the member.
For design of section 39.5 and 39.6 as appropriate shall apply.
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NOTES-
1. A column may be considered braced in a given plane if lateral stability to the structure as a whole is provided by walls or bracing or buttressing designed to resist all lateral forces in that plane, it should otherwise be considered as embraced.
2.In the case of a braced column without any transverse loads occurring in its height, the additional moment shall be added to an initial moment equal to sum of 0.4 M_a1 and 0.6 M_a2where M_a2 is the larger end moment andM_a1 is the smaller end moment (assumed negative if the column is bent in double curvature). In no case shall the initial moment be less than 0.4M_a2 nor the total moment including the initial moment be less than M_a2. For unbraced columns, the additional moment shall be added to the end moments.
3.Unbraced compression members, at any given level storey, subject to lateral load are usually constrained to deflect equally. In such cases slenderness ratio for each column may be taken as the average for all columns acting in the direction.
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→The values given by equation 39.7.1 may be multiplied by the following factors
k=(P_ux-P_a)/(P_ux-P_b )≤1
Where
P_a= Axial load on compression member
P_ux = as defined in 39.6 and
P_b= Axial load corresponding to the direction of maximum compressive strain of 0.003 5 in concrete and tensile strain of 0.002 in outer most layer of tension steel.
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| 40. LIMIT STATE OF COLLAPSE: SHEAR |
40.1 Nominal Shear Stress |
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The nominal shear stress in beams of uniform depth shall be obtained by the following equations:
τ_v=V_u/b_d
Where
V_u=Shear force due to design looks;
b=breadth of the member,which forflanged section shall be taken
as the breadth of the web b.and
d=effective depth.
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1. Beams of Varying Depth
In the case of beams of varying depth the equations shall be modified as:
τ_v = (V_u±M_u/d tanβ)/bd
Where
τ_v,V_u,b and d are the same as in 40.1
M_u=bending moment at the section and
β=angle between the top and the bottom edges
The negative sign in the formula applies when the bending moment M_u increases numerically in the same direction as the effective depth d increases and the positive sign when the moment decreases numerically in the direction.
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40.2 Design shear Strength of Concrete |
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1. The design shear strength of concrete in beams without shear reinforcement is given in table 19
For solid slabs , the design Shear strength for concrete shall be τ_c k where k has the values given below:
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Overall Depth of slab, mm |
300 or more |
275 |
250 |
225 |
200 |
175 |
150 or less |
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k |
1 |
1.05 |
1.1 |
1.15 |
1.2 |
1.25 |
1.3 |
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Note- This provision shall not apply to flat slabs for which 31.6 shall apply |
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2. Shear strength of Members under Axial compression
For members subjected to axial compression P_u, the design shear strength of concrete, given in table 19 shall be multiplied by the following factors:
δ=1+(3P_u)/(A_g f_ck ) but not exceeding 1.5
Where
P_u= Axial compressive force in Newton
A_g=gross area of the concrete section in mm^2
f_ck=characteristics compressive strength of concrete
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3. With Shear Reinforcement
Under no circumstances, even with shear reinforcement, shall the nominal shear stress in beams
τ_v exceed τ_cmax given in table 20
→For solids slabs, the nominal shear stress shall not exceed half the appropriate values given in table 20
Maximum shear stress τ_cmax given in table 20 is valid for all load cases including earthquake except the following:
a)For coupling beams in coupled shear walls. Under earthquake forces, the limiting values of τ_cmax given in table 20 shall be suspended by 10 of IS 1392:2016.
b)Coupled shear walls shall be connected by ductile coupling beams. If the earthquake induced shear stress un the coupling beam exceeds
(0.1l_s √(f_ck ))/(D )
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Table 20 Maximum Shear stress τ_cmax, N/mm2
(clause 40.2.3, 40.2.3.1, 40.5.1 and 41.3.1) |
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Concrete Grade |
M15 |
M20 |
M25 |
M30 |
M35 |
M40 and above |
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2.5 |
2.8 |
3.1 |
3.7 |
3.7 |
4 |
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Where l_s is the clear span of the coupling beam and D is its overall depth, the entire earth quake induced shear and flexure shall, preferably, be resisted by diagonal reinforcement.
The area of reinforcement to be provided along each diagonal in a diagonally reinforced coupling beam shall be
A_sd=V_u/(1.74f_y sinα)
Where V_u is the factored shear force and α is the angle made by the diagonal reinforcement with the horizontal. At least 4 bars of 8mm diameter shall be provided along each diagonal. The reinforcement along each diagonal shall be enclosed by special confining reinforcement, as per 8 of IS 13920: 2016. The pitch of spiral or spacing of ties shall not exceed 100mm.
The diagonal or horizontal bars of a coupling beam shall be anchored in the adjacent walls with an anchorage length of 1.5 times the development length in tension. |
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40.3 Minimum Shear Reinforcement |
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When τ_v is less than τ_c given in table 19, minimum shear reinforcement shall be provided in
accordance with 26.5.1 |
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Table 19 Design Shear Strength of Concrete, τ_c,N/〖mm〗^2
(Clause 40.2.1, 40.2.2, 40.3, 40.4, 40.5.3, 41.5.3, 41.3.2. 41.3.3 and 41.4.3) |
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100 X |
Concrete Grade |
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M15 |
M20 |
M25 |
M30 |
M35 |
M40 and Above |
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-1 |
-2 |
-3 |
-4 |
-5 |
-6 |
-7 |
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0.28 |
0.28 |
0.29 |
0.29 |
0.29 |
0.3 |
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0.25 |
0.35 |
0.36 |
0.36 |
0.37 |
0.37 |
0.38 |
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0.5 |
0.46 |
0.48 |
0.49 |
0.5 |
0.5 |
0.51 |
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0.75 |
0.54 |
0.56 |
0.57 |
0.59 |
0.59 |
0.6 |
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1 |
0.6 |
0.62 |
0.64 |
0.66 |
0.67 |
0.68 |
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1.25 |
0.64 |
0.67 |
0.7 |
0.71 |
0.73 |
0.74 |
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1.5 |
0.71 |
0.72 |
0.74 |
0.76 |
0.78 |
0.79 |
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1.75 |
0.71 |
0.75 |
0.78 |
0.8 |
0.82 |
0.84 |
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2 |
0.71 |
0.79 |
0.82 |
0.84 |
0.86 |
0.88 |
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2.25 |
0.71 |
0.81 |
0.85 |
0.88 |
0.9 |
0.92 |
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2.5 |
0.71 |
0.82 |
0.88 |
0.91 |
0.93 |
0.95 |
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2.75 |
0.71 |
0.82 |
0.9 |
0.94 |
0.96 |
0.98 |
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3.00and above |
0.71 |
0.82 |
0.92 |
0.96 |
0.99 |
1.01 |
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NOTE-
The term A_c is the area of longitudinal tension reinforcement which continues at least one effective depth beyond the section being considered except support where the full area of tension reinforcement may be used. |
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40.4 Design of Shear Reinforcement |
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When τ_v exceeds τ_c given in table 19, shear reinforcement shall be provided in any of the following forms:
a) vertical stirrups
b) Bent-up bas along with stirrups and
c) Inclined Stirrups
Where bent-up bars are provided, their contribution towards shear resistance shall not be more than half that of the total shear reinforcement.
Shear reinforcement shall be provided to carry a shear equal to V_u-τ_c bd The strength of shear reinforcement V_us shall be calculated as below
a) For vertical stirrups
V_us = (0.87f_y A_sv d)/S_v
b) For inclined stirrups or a series of bars bent-up at different cross-sections:
V_us=(0.87f_y A_sv d)/S_v ( sinα+cosα)
c) For single bar or single group of parallel bars, all bent- up at the same cross-sections:
V_us=0.87f_y A_sv sinα
Where
A_sv= total cross-sectional area of stirrup legs or bent-up bars or distance S_v
S_v= Spacing stirrups or bent-up bars along the length of the member
τ_v= Nominal shear stress,
τ_c= design shear strength of the concrete
b= breadth of the member which for flanged beams, shall be taken as the breadth of the web〖 b〗_w
f_y= characteristics strength of the stirrup or bent-up reinforcement which shall not be taken greater than 415N/mm2
α= angle between the inclined stirrup or bent- up bar and the axis of the member, not less than 45° and
d=effective depth
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| 41. LIMIT STATE OF COLLAPSE: TORSION |
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NOTE- The approach to design in this clause is as follows:
Torsional reinforcement is not calculated separately from that required for bending and shear. Instead the total longitudinal reinforcement is determined for a fictitious bending moment which is a function of actual bending moment and torsion; similarly web reinforcement is determined for a fictitious shear which is a functional of actual shear and torsion.
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→ The design rules laid down in 41.3 and 41.4 shall be apply to beams of solid rectangular cross-sections.
However, these clauses may also be applied to flanged beams, by substituting b_w for b in which case they are generally conservative; therefore specialist literature may be referred to. |
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41.2 Critical Section
Sections located less than a distance d, from the face of the support may be designed for the same torsion as computed at a distance d, where d is the effective depth. |
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41.3 Shear and Torsion
→ Equivalent Shear
Equivalent shear, V_e ,shall be calculated from the formula
V_e=V_u+1.6 T_u/b
Where
V_e=equiavlent shear
V_u=shear
T_u=torsional moment,and
b=breadth of beam
The equivalent nominal shear stress, τ_ve in this case shall be calculated as given in 40.1, expect for substitutingV_u and V_e. The value of τ_ve shall not exceed the values of τ_cmax given in table 20.
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41.4 Reinforcement in Members
Subjected to Torsion |
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1. Longitudinal Reinforcement
The longitudinal reinforcement shall be designed to resist an equivalent bending moment M_e1, given by
M_e1=M_b+M_t
Where
M_b= bending moment at the cross-section, and
M_t= T_o ((1D/b)/1.7)
Where T_o is the torsional moment, D is the overall depth of the beam and b is the breadth of the beam.
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2. Transverse Reinforcement
Two Legged closed hoops enclosing the corner longitudinal bars shall have an area of cross-section Asv given by
Asv = (T_u S_v)/(b_1 d_1 (0.87f_y))+(V_u S_v)/(2.5d_1 (0.87f_y))
But the total transverse reinforcement shall not be less than
((τ_ve-τ_c )b.s_v)/(0.87f_y )
Where
T_u=torsional moment,
V_u=shear force
s_v=spacing of the stirrup reinforcement
b_1=centre to centre distance between corner bars
d_1=centre-to-centre distance between corner bars,
b=breadth of the members,
f_(y )=characteristics strength of the stirrup reinforcement
τ_ve=equivalent shear stress as specified in 41.3.1 and
τ_c=shear strength of the concrete as per Table 19.
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| 42 LIMIT STATE OF SERVICEABILITY:
DEFELECTION |
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42.1 Flexural Members
In all normal cases, the deflection of a flexural member will not be excessive if the ratio of its span to its effective depth is not greater than appropriate ratios given in 23.2.1. When deflection are calculated according to Annex C, they shall not exceed the permissible values given in 23.2
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| 43 Limit State of Serviceability: Cracking |
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43.1 Flexural Members
In general, compliance with the spacing requirements of reinforcement given in 26.3.2 should be sufficient to control Flexural cracking. If greater spacing are required, the expected crack width should be checked by formula given in Annex F.
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43.2 Compression Members
Cracks due to bending in a compression members subjected to a design axial load greater than 〖0.2f〗_ck A_c' where f_ck is the characterictics compressive strength of concrete and A_c is the area of the gross section of the member need to be checked. A member subjected to lesser load than 〖0.2f〗_ck A_c may be considered as flexural member for the purpose of crack control (see43.1)
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