Strength of hardened concrete
Introduction
A) Definition
Strength is defined as the ability of a material to resist stress without failure. The failure of concrete is due to cracking. Under direct tension, concrete failure is due to the propagation of a single major crack. In compression, failure involves the propagation of a large number of cracks, leading to a mode of disintegration commonly referred to as ‘crushing’. The strength is the property generally specified in construction design and quality control, for the following reasons:
(1) It is relatively easy to measure, and (2) other properties are related to the strength and can be deduced from strength data. The 28-day compressive strength of concrete determined by a standard uniaxial compression test is accepted universally as a general index of concrete strength.
Compressive strength and corresponding tests
a) Failure mechanism
The development of the vertical cracks results in expansion of concrete in the lateral directions. If concrete is confined (i.e., it is not allowed to expand freely in the lateral directions), growth of the vertical cracks will be resisted. The strength is hence increased, together with an increase in failure strain. In the design of concrete columns, steel stirrups are placed around the vertical reinforcing steel. They serve to prevent the lateral displacement of the interior concrete and hence increase the concrete strength. In composite construction (steel + reinforced concrete), steel tubes are often used to encase reinforced concrete columns. The tube is very effective in providing the confinement.
(b) Specimen for compressive strength determination
Note that the cube specimen is popular in U.K. and Europe while the cylinder specimen is commonly used in the U.S.
i) Cube specimen
BS 1881: Part 108: 1983.Filling in 3 layers with 50 mm for each layer (2 layers for 100 mm cube). Strokes 35times for 150 mm cube and 25 times for 100 mm cube. Curing at 20±50C and 90% relative humility.
ii) Cylinder specimen
ASTM C470-81. Standard cylinder size is 150 x 300 mm. Curing condition is temperature of 23±1.70C and moist condition. Grinding or capping is needed to provide level and smooth compression surface.
(c) Factors influencing experiment results
(i) End condition. Due to influence of platen restraint, cube's apparent strength is about 1.15 times of cylinders. In assessing report on concrete strength, it is important to know which type of specimen has been employed.
(ii) Loading rate. The faster the load rate, the higher the ultimate load obtained. The standard load rate is 0.15 -0.34 MPa / s for ASTM and 0.2-0.4 MPa/s for BS.
(iii)Size effect: The probability of having larger defects (such as voids and cracks) increases with size. Thus, smaller size specimen will give higher apparent strength.
Tensile strength and corresponding tests
It is important to notice that cracks form and propagate a lot easier in tension than in compression. The tensile strength is hence much lower than the compressive strength.
a) Direct tension test methods
Direct tension tests of concrete are seldom carried out because it is very difficult to control. Also, perfect alignment is difficult to ensure and the specimen holding devices introduce secondary stress that cannot be ignored. In practice, it is common to carry out the splitting tensile test or flexural test.
b) Indirect tension test (split cylinder test or Brazilian test)
The splitting test is carried out by applying compression loads along two axial lines that are diametrically opposite. This test is based on the following observation from elastic analysis. Under vertical loading acting on the two ends of the vertical diametrical line, uniform tension is introduced along the central part of the specimen. The splitting tensile strength can be obtained using the following formula:
Fst=2P/πLD
According to the comparison of test results on the same concrete, fst is about 10-15% higher than direct tensile strength, ft.
c) Flexural strength and corresponding tests
Flexural test; 150 x 150 x 750 mm or 100 x 100 x 500 (Max. size of aggregate is less than 25 mm). From Mechanics of Materials, we know that the maximum tension stress should occur at the bottom of the constant moment region.
The modulus of rapture can be calculated as:
Fbt=PL/(bd*d)
This formula is for the case of fracture taking place within the middle one third of the beam. If fracture occurs outside of the middle one-third (constant moment zone), the modulus of rupture can be computed from the moment at the crack location according to ASTM standard, with the following formula.
Fbt=3Pa/(bd*d)
However, according to British Standards, once fracture occurs outside of the constant moment zone, the test result should be discarded. Although the modulus of rupture is a kind of tensile strength, it is much higher than the results obtained from a direct tension test. This is because concrete can still carry stress after a crack is formed. The maximum load in a bending test does not correspond to the start of cracking, but correspond to a situation when the crack has propagated. The stress distribution along the vertical section through the crack is no longer varying in a linear manner. The above equations are therefore not exact.
CONCRETE MIXES
Tables 1-6 show the most common mixes for different volumes of concrete and for different parts of concrete structures.
Table 1: volume of concrete produced from 50kg cement
Mix volume of concrete
1:3:6 0.24
1:2:4 0.17
1:5:3 0.13
Table 2: quantity of materials required to produce 1m3 of concrete.
Mix Cement (kg) Sand(m3) Aggregate(m3)
1:3:6 172 0.36 0.72
1:2:4 238 0.33 0.67
1:5:3 299 0.13 0.62
Table3: approximate volumes for buckets
Mix Cement(buckets) Sand(buckets) Aggregate(buckets) Water(buckets)
1:3:6 1 3 6 0.75
1:2:4 1 2 4 0.5-0.75
1:5:3 1 0.5 3 0.5
Table 4: water and cement ratio for normal slump
Mix water and cement ratio liter of water for 50kg cement
1:3:6 0.7 36
1:2:4 0.55 27
1:5:3 0.5 25
Table 5: mixes for different concrete structures
Mix Structures Cement(kg) Sand(m3) Aggregate(m3) Water(litre)
1:3:6 Mass foundations, 50 0.11 0.212 36
1:3:6 Oversite slabs 50 0.11 0.212 36
1:2:4 General reinforced concrete work 50 0.07 0.413 30
Table6: maximum slump for concrete structures
Concrete structure Maximum slump(mm)
Mass foundation 76
Reinforced foundation 100
Oversite concrete 125
Reinforced slabs and beams 125
Reinforced column 100
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