Question

Design a plain concrete mix required for 400mm deep RCC beam to be constructed in New Girls Hostel at GIK Institute (you can assume workability). The specified compressive strength is 32 MPa at 28 days. The standard deviation of the concrete producer is 3.0 MPa. Select nominal maximum-size coarse aggregate from following data

1. Min. distance b/w two reinforcing bar is 40mm
2. Min. distance b/w reinforcing bar and concrete surface (clear cover) is 42mm
3. Thick of slab is 120mm
4. Concrete is not pump-able

The specific gravity of fine aggregate (FA) and coarse aggregate (C.A) are 2.5 and 2.6 respectively. The dry rodded bulk density of C.A. is 1650 kg/m3, and fineness modulus (FM) of FA is 2.70.

C.A. is found to be absorptive to the extent of 5 % and free surface moisture (moisture content) in sand is found to be 5 per cent .Assume any other essential data, concrete should be durable against sulfate and chloride attack.

Answer 1

• Specified Compressive strength is 32 MPa at 28 days with a standard deviation of 3 MPa.
• distance between reinforcement = 40 mm
• clear cover for reinforcement = 42mm
• nonpumpable concrete
• SFA = 2.5 , SCA = 2.6 Bulk density of CA = 1650 kg/m3,
• fineness modulus of FA = 2.7
• CA absorbs water to the extent of 5%,
• moisture content in sand is 5 %
• concrete should be durable against sulfate and chloride

Now,

fck = 32 MPa , S = 3 MPa

Target mean strength = f'ck = fck + 1.65*S = 32 + 1.65 * 3 = 36.95 MPa

Studies were confined mostly to the deterioration of concrete structures under single deteriorating factor such as chloride ingress only or sulfate attack only, although the real environment is actually a combination of such factors.

So, the exposure condition of concrete is "very severe" i.e. max w/c = 0.45 and concrete for slabs and beams should have slump of 40 to 50 mm.

Gap between reinforcement bars is 40mm and clear cover is 42mm,

therefore, nominal size aggregate of 20 mm can be used.

Water Content  

for 20mm nominaal size aggregate, wwater contnet = 186kg/m3 of concrete for slump 25-50mm..

Cement contenet

w/c = 0.45, thus cement = 186/0.45 = 413 kg/m3 ( >> than minimum requirement of 3400kg/m3 of very severe exposure condition , ..ok).

Fineness modulus of san is 2.7 i.e it is medium sand of zone II,

thus, volume of coarse aggregate per unit volume o concrete is 0.62 for 20mm at w/c ratio of 0.5 but actual is 0.45 - 0.05 less therefore, 0.01% of aggregate percentage is incresed

thus percentaage of CA = 0.62+0.01 = 0.72%

so, volumeo of FA = 1-0.72 = 0.28 times volume of total aggregates.

VA = 1- [ C/Sc + W/1]/1000 = 1 - [ 413/3.15 + 186/1]/1000 = 0.683 kg/m3

VCA = 0.72*0.683 = 0.49 kg/m3 MCA = 2.6 * 0.49 *1000= 1274 kg/m3

VFA = 0.19 kg/m3 MFA = 2.5 * 0.19 * 1000 = 479 kg/m3

but it is given that CA absorbs 5% and sand has moisture contenet of 5 %

then , water contenet = 186 + 5 % * 1274 - 5%* 479 = 186 + 63.7 - 23.95 = 225.75 kg/m3

corrected mass of CA = 1274-63.7 = 1210 kg/m3

corrected mass of FA = 479+23.95 = 503 kg/m3

cement = 413kg/m3

water = 225.75kg/m3

w/c = 225.75/413 = 0.54