Saturday, July 4, 2009

Concrete Mix Design Calculations

The concrete mix design available on this site are for reference purpose only. Actual site conditions vary and thus this should be adjusted as per the location and other factors. These are just to show you how to calculate and we are thankful to all the members who have emailed us these mix designs so that these could be shared with civil engineers worldwide.

If you also have any mix design and want to share it with us, just comment on this post and we will be in touch with you.

Here is the summary of links of all the mix designs we have till date:-

Mix Design For M20 Grade Of Concrete

Mix Design For M35 Grade Of Concrete

Mix Design For M40 Grade Of Concrete

Mix Design For M50 Grade Of Concrete

Mix Design For M60 Grade Of Concrete

In case you want the complete theory of Mix Design, Go here What is Concrete Mix Design

We will add more soon. You can help us do this fast, just email us any mix design you have.

Mix Design M-50 Grade

The mix design M-50 grade (Using Admixture –Sikament) provided here is for reference purpose only. Actual site conditions vary and thus this should be adjusted as per the location and other factors.

Parameters for mix design M50

Grade Designation = M-50
Type of cement = O.P.C-43 grade
Brand of cement = Vikram ( Grasim )
Admixture = Sika [Sikament 170 ( H ) ]
Fine Aggregate = Zone-II

Sp. Gravity
Cement = 3.15
Fine Aggregate = 2.61
Coarse Aggregate (20mm) = 2.65
Coarse Aggregate (10mm) = 2.66

Minimum Cement (As per contract) =400 kg / m3
Maximum water cement ratio (As per contract) = 0.45

Mix Calculation: -

1. Target Mean Strength = 50 + ( 5 X 1.65 ) = 58.25 Mpa

2. Selection of water cement ratio:-
Assume water cement ratio = 0.35

3. Calculation of water: -
Approximate water content for 20mm max. Size of aggregate = 180 kg /m3 (As per Table No. 5 , IS : 10262 ). As plasticizer is proposed we can reduce water content by 20%.

Now water content = 180 X 0.8 = 144 kg /m3

4. Calculation of cement content:-
Water cement ratio = 0.35
Water content per cum of concrete = 144 kg
Cement content = 144/0.35 = 411.4 kg / m3
Say cement content = 412 kg / m3 (As per contract Minimum cement content 400 kg / m3 )
Hence O.K.

5. Calculation for C.A. & F.A.: [ Formula's can be seen in earlier posts]-

Volume of concrete = 1 m3
Volume of cement = 412 / ( 3.15 X 1000 ) = 0.1308 m3
Volume of water = 144 / ( 1 X 1000 ) = 0.1440 m3
Volume of Admixture = 4.994 / (1.145 X 1000 ) = 0.0043 m3
Total weight of other materials except coarse aggregate = 0.1308 + 0.1440 +0.0043 = 0.2791 m3

Volume of coarse and fine aggregate = 1 – 0.2791 = 0.7209 m3
Volume of F.A. = 0.7209 X 0.33 = 0.2379 m3 (Assuming 33% by volume of total aggregate )

Volume of C.A. = 0.7209 – 0.2379 = 0.4830 m3

Therefore weight of F.A. = 0.2379 X 2.61 X 1000 = 620.919 kg/ m3

Say weight of F.A. = 621 kg/ m3

Therefore weight of C.A. = 0.4830 X 2.655 X 1000 = 1282.365 kg/ m3

Say weight of C.A. = 1284 kg/ m3

Considering 20 mm: 10mm = 0.55: 0.45
20mm = 706 kg .
10mm = 578 kg .
Hence Mix details per m3
Increasing cement, water, admixture by 2.5% for this trial

Cement = 412 X 1.025 = 422 kg
Water = 144 X 1.025 = 147.6 kg
Fine aggregate = 621 kg
Coarse aggregate 20 mm = 706 kg
Coarse aggregate 10 mm = 578 kg
Admixture = 1.2 % by weight of cement = 5.064 kg.

Water: cement: F.A.: C.A. = 0.35: 1: 1.472: 3.043

Observation: -
A. Mix was cohesive and homogeneous.
B. Slump = 120 mm
C. No. of cube casted = 9 Nos.
7 days average compressive strength = 52.07 MPa.
28 days average compressive strength = 62.52 MPa which is greater than 58.25MPa
Hence the mix accepted.

Mix Design M-40 Grade

The mix design M-40 grade for Pier (Using Admixture – Fosroc) provided here is for reference purpose only. Actual site conditions vary and thus this should be adjusted as per the location and other factors.

Parameters for mix design M40

Grade Designation = M-40
Type of cement = O.P.C-43 grade
Brand of cement = Vikram ( Grasim )
Admixture = Fosroc ( Conplast SP 430 G8M )
Fine Aggregate = Zone-II
Sp. Gravity Cement = 3.15
Fine Aggregate = 2.61
Coarse Aggregate (20mm) = 2.65
Coarse Aggregate (10mm) = 2.66
Minimum Cement (As per contract) = 400 kg / m3
Maximum water cement ratio (As per contract) = 0.45

Mix Calculation: -

1. Target Mean Strength = 40 + (5 X 1.65) = 48.25 Mpa

2. Selection of water cement ratio:-
Assume water cement ratio = 0.4

3. Calculation of cement content: -
Assume cement content 400 kg / m3
(As per contract Minimum cement content 400 kg / m3)

4. Calculation of water: -
400 X 0.4 = 160 kg Which is less than 186 kg (As per Table No. 4, IS: 10262)
Hence o.k.

5. Calculation for C.A. & F.A.: - As per IS : 10262 , Cl. No. 3.5.1

V = [ W + (C/Sc) + (1/p) . (fa/Sfa) ] x (1/1000)

V = [ W + (C/Sc) + {1/(1-p)} . (ca/Sca) ] x (1/1000)

Where

V = absolute volume of fresh concrete, which is equal to gross volume (m3) minus the volume of entrapped air ,

W = mass of water ( kg ) per m3 of concrete ,

C = mass of cement ( kg ) per m3 of concrete ,

Sc = specific gravity of cement,

(p) = Ratio of fine aggregate to total aggregate by absolute volume ,

(fa) , (ca) = total mass of fine aggregate and coarse aggregate (kg) per m3 of
Concrete respectively, and

Sfa , Sca = specific gravities of saturated surface dry fine aggregate and Coarse aggregate respectively.

As per Table No. 3 , IS-10262, for 20mm maximum size entrapped air is 2% .

Assume F.A. by % of volume of total aggregate = 36.5 %

0.98 = [ 160 + ( 400 / 3.15 ) + ( 1 / 0.365 ) ( Fa / 2.61 )] ( 1 /1000 )

=> Fa = 660.2 kg

Say Fa = 660 kg.

0.98 = [ 160 + ( 400 / 3.15 ) + ( 1 / 0.635 ) ( Ca / 2.655 )] ( 1 /1000 )

=> Ca = 1168.37 kg.

Say Ca = 1168 kg.

Considering 20 mm : 10mm = 0.6 : 0.4

20mm = 701 kg .
10mm = 467 kg .

Hence Mix details per m3

Cement = 400 kg
Water = 160 kg
Fine aggregate = 660 kg
Coarse aggregate 20 mm = 701 kg
Coarse aggregate 10 mm = 467 kg
Admixture = 0.6 % by weight of cement = 2.4 kg.
Recron 3S = 900 gm

Water: cement: F.A.: C.A. = 0.4: 1: 1.65: 2.92

Observation: -
A. Mix was cohesive and homogeneous.
B. Slump = 110mm
C. No. of cube casted = 12 Nos.
7 days average compressive strength = 51.26 MPa.
28 days average compressive strength = 62.96 MPa which is greater than 48.25MPa

Hence the mix is accepted.


Concrete Mix Design - M 20 Grade Of Concrete


1. REQUIREMENTS
a) Specified minimum strength = 20 N/Sq mm

b) Durability requirements
i) Exposure Moderate
ii) Minimum Cement Content = 300 Kgs/cum

c) Cement
(Refer Table No. 5 of IS:456-2000)
i) Make Chetak (Birla)
ii) Type OPC
iii) Grade 43

d) Workability
i) compacting factor = 0.7

e) Degree of quality control Good

Concrete Mix Design M-60


CONCRETE MIX DESIGN (GRADE M60)


(a) DESIGN STIPULATION:-
Target strength = 60Mpa
Max size of aggregate used = 12.5 mm
Specific gravity of cement = 3.15
Specific gravity of fine aggregate (F.A) = 2.6
Specific gravity of Coarse aggregate (C.A) = 2.64
Dry Rodded Bulk Density of fine aggregate = 1726 Kg/m3
Dry Rodded Bulk Density of coarse aggregate = 1638 Kg/m3

Plate Girder In Buildings

or greatest resistance to bending, as much of a plate girder cross section as practicable should be concentrated in the flanges, at the greatest distance from the neutral axis. This
might require, however, a web so thin that the girder would fail by web buckling before it reached its bending capacity.

To preclude this, the AISC specification limits h/t.

For an unstiffened web, this ratio should not exceed.
h / t = 14,000 / (F Y (F y + 16.5) ) ½
where F y = yield strength of compression flange, ksi (MPa).

Larger values of h/t may be used, however, if the web is stiffened at appropriate intervals.

For this purpose, vertical angles may be fastened to the web or vertical plates welded to it. These transverse stiffeners are not required, though, when h/t is less than the value
computed from the preceding equation or Table 9.4.

Critical h/t for Plate Girders in Buildings should be taken from the codes

With transverse stiffeners spaced not more than 1.5 times the girder depth apart, the web clear-depth/thickness ratio may be as large as
h / t = 2000 / ( F y ) ½
If, however, the web depth/thickness ratio h/t exceeds 760 / (F b ) ½ , where F b , ksi (MPa), is the allowable bending stress in the compression flange that would ordinarily apply, this stress should be reduced to F ‘ b , given by the following equations:

F ‘ b = R P G R e F ¬b
R P G = [ 1 – 0.0005 ( A w / A f ) ( h/t – 760 / ( F b )) ½ ] ? 1.0

R e = [ ( 12 + ( A w /A f ) (3a – a 3 ) ) / ( 12 + 2 (A w / A f ) ] ? 1.0

Where A w = web area , in 2 (mm 2 )

A f = area of compression flange, in 2 (mm 2 )

a = 0.6 F y w / F b ? 1.0

F y w = minimum specified yield stress, ksi, (MPa), of web steel

In a hybrid girder, where the flange steel has a higher yield strength than the web, the preceding equation protects against excessive yielding of the lower strength web in the vicinity of the higher strength flanges. For nonhybrid girders, R e = 1.0.

Deflections of Bents and Shear Walls


Horizontal deflections in the planes of bents and shear walls can be computed on the assumption that they act as cantilevers. Deflections of braced bents can be calculated
by the dummy-unit-load method or a matrix method. Deflections of rigid frames can be computed by adding the drifts of the stories, as determined by moment distribution
or a matrix method.

For a shear wall (Fig) the deflection in its plane induced by a load in its plane is the sum of the flexural
Figure showing Building frame resists lateral forces with (a) wind bents or (g) shear walls or a combination of the two. Bents may be braced in any of several ways, including (b) X bracing, (c) K bracing, (d) inverted V bracing, (e) knee bracing, and (f) rigid connections.

deflection as a cantilever and the deflection due to shear. Thus, for a wall with solid rectangular cross section, the deflection at the top due to uniform load is

? = 1.5 wH / Et [ ( H / L ) 3 + H / L]

where w = uniform lateral load

H = height of the wall

E = modulus of elasticity of the wall material

t = wall thickness

L = length of wall

For a shear wall with a concentrated load P at the top, the deflection at the top is

? c = ( 4 P / Et ) [ ( H / L ) 3 + 0.75 H / L ]

If the wall is fixed against rotation at the top, however, the deflection is

? f = ( P / Et ) [ ( H / L ) 3 + 3 H / L ]

Units used in these equations are those commonly applied in United States Customary System (USCS) and the System International (SI) measurements, that is, kip (kN), lb /in 2 (MPa), ft (m), and in (mm).

Where shear walls contain openings, such as those for doors, corridors, or windows, computations for deflection and rigidity are more complicated. Approximate methods, however, may be used.

Combined Axial Compression Or Tension And Bending

The AISC specification for allowable stress design for buildings includes three interaction formulas for combined axial compression and bending.

When the ratio of computed axial stress to allowable axial stress f /F a exceeds 0.15, both of the following equations must be satisfied:

( f a / F a ) + ( C m x f b x ) / (1– f a /F ‘ e x ) F b x + C m y f b y / (1 – f a / F ‘ e y ) F b y ? 1

f a / 0.60F y + f b x /F b x + f b y / F b y ? 1

when f a /F a ? 0.15, the following equation may be used instead of the preceding two:

f a / F a + f b x / F b x + f b y / F b y ? 1

In the preceding equations, subscripts x and y indicate the axis of bending about which the stress occurs, and

In the preceding equations, subscripts x and y indicate the axis of bending about which the stress occurs, and

F a = axial stress that would be permitted if axial force alone existed, ksi (MPa)

F b = compressive bending stress that would be permitted if bending moment alone existed, ksi (MPa)

F ‘ e = 149,000 / ( Kl b / r b ) 2 , ksi (MPa); as for F a , F b , and 0.6F y , F ‘ e may be increased one-third for wind and seismic loads

Lb = actual unbraced length in plane of bending, in (mm)

r b = radius of gyration about bending axis, in (mm)

K = effective-length factor in plane of bending

f a = computed axial stress, ksi (MPa)

f b = computed compressive bending stress at point under consideration, ksi (MPa)

C m = adjustment coefficient

WEBS UNDER CONCENTRATED LOADS

Criteria for Buildings

The AISC specification for ASD for buildings places a limit on compressive stress in webs to prevent local web yielding. For a rolled beam, bearing stiffeners are required at a concentrated load if the stress f a , ksi (MPa), at the toe of the web fillet exceeds F a = 0.66F y w , where F y w is the minimum specified yield stress of the web steel, ksi (MPa). In the calculation of the stressed area, the load may be assumed distributed over the distance indicated in Fig. 9.4.

For a concentrated load applied at a distance larger than the depth of the beam from the end of the beam:

F a = R / f w ( N + 5K )

where R = concentrated load of reaction, kip (kN)

t w = web thickness, in (mm)

N = length of bearing, in (mm), (for end reaction, not less than k)

K = distance, in (mm), from outer face of flange to web toe of fillet

For a concentrated load applied close to the beam end:

f a = R / t w ( N + 2.5 k )

To prevent web crippling, the AISC specification requires that bearing stiffeners be provided on webs where concentrated loads occur when the compressive force
exceeds R, kip (kN), computed from the following:

For a concentrated load applied at a distance from the beam end of at least d/2, where d is the depth of beam:

R = 67.5 t 2 w [ 1 + 3 ( N / d ) ( t w / t f ) 1.5 ] (F y w t f / t w ) ½

where t f = flange thickness, in (mm)

For a concentrated load applied closer than d/2 from the beam end:

R = 34r 2 w [ 1 + 3 ( N / d ) ( t w / t f ) 1.5 ] ( F y w t f / t w ) ½

If stiffeners are provided and extend at least one-half of the web, R need not be computed.

Another consideration is prevention of sidesway web buckling. The AISC specification requires bearing stiffeners when the compressive force from a concentrated load
exceeds limits that depend on the relative slenderness of web and flange r w f and whether or not the loaded flange is restrained against rotation:

r w f = ( d c / t w ) / ( l / b f )

where l = largest unbraced length, in (mm), along either top or bottom flange at point of application of load

b = flange width, in (mm)

d c = web depth clear of fillets = d – 2k

Stiffeners are required if the concentrated load exceeds R, kip (kN), computed from

R = 6800 t 3 w / h ( 1 + 0.4 r 3 w f )

where h = clear distance, in (mm), between flanges, and r w f
is less than 2.3 when the loaded flange is restrained against rotation. If the loaded flange is not restrained and r w f is less than 1.7,

R = 0.4 r 3 w f ( 6800 t 3 w / h )

R need not be computed for larger values of r w f ..

DESIGN OF STIFFENERS UNDER LOADS

AISC requires that fasteners or welds for end connections of beams, girders, and trusses be designed for the combined effect of forces resulting from moment and shear induced by the rigidity of the connection. When flanges or moment connection plates for end connections of beams and girders are welded to the flange of an I- or H-shape column, a pair of column-web stiffeners having a combined cross-sectional area A s t not less than that calculated from the following equations must be provided whenever the calculated value of A s t is positive:

A s t = ( P b f – F y c t w c ( t b + 5k ) ) / F y s t

where F y c = column yield stress, ksi (MPa)

F y s t = stiffener yield stress, ksi (MPa)

K = distance, in (mm), between outer face of column flange and web toe of its fillet, if column is rolled shape, or equivalent distance if column is welded shape

P b f = computed force, kip (kN), delivered by flange of moment-connection plate multi plied by 5/3 , when computed force is due to live and dead load only, or by 4/3, when computed force is due to live and dead load in conjunction with wind or earthquake forces

T w c = thickness of column web, in (mm)

T b = thickness of flange or moment-connection plate delivering concentrated force, in (mm)

Notwithstanding the preceding requirements, a stiffener or a pair of stiffeners must be provided opposite the beam compression flange when the column-web depth clear of fillets d c is greater than

d c = ( 4100 t 3 w c ( F y e ) ½ ) / P b f

and a pair of stiffeners should be provided opposite the tension flange when the thickness of the column flange t f is less than

t f = 0.4 ( P b f ) ½ / F y c

Stiffeners required by the preceding equations should comply with the following additional criteria:

1. The width of each stiffener plus half the thickness of the column web should not be less than one-third the width of the flange or moment-connection plate delivering the concentrated force.

2. The thickness of stiffeners should not be less than t b /2.

3. The weld-joining stiffeners to the column web must be sized to carry the force in the stiffener caused by unbalanced moments on opposite sides of the column.

FASTENERS IN BUILDINGS

The AISC specification for allowable stresses for buildings specifies allowable unit tension and shear stresses on the cross-sectional area on the unthreaded body area of bolts and threaded parts. (Generally, rivets should not be used in direct tension.) When wind or seismic load are combined with gravity loads, the allowable stresses may be increased one-third.

Most building construction is done with bearing-type connections. Allowable bearing stresses apply to both bearing-type and slip-critical connections. In buildings, the allowable bearing stress F p , ksi (MPa), on projected area of fasteners is

F p = 1.2 F

where F ­u is the tensile strength of the connected part, ksi (MPa). Distance measured in the line of force to the nearest edge of the connected part (end distance) should be at least 1.5d, where d is the fastener diameter. The center-to-center spacing of fasteners should be at least 3d.