Reinforced Concrete Design

Chapter 01 Reinforced Concrete Design

Chapter 01 Reinforced Concrete Design

REFERENCESJack C. McCormac and James K. Nelson, Design of Reinforced Concrete 8th Edition, John Wiley & Sons Inc. 2006Arthur H. Nilson, David Darwin and Charles W. Dolan, Design of Concrete Structures, Fourteenth Edition in SI units, Mc Graw Hill, 2010Leonard Spiegel and George F. Limbrunner, Reinforced Concrete Design 4th Edition, Prentice Hall Association of Structural Engineers of the Philippines Inc. (ASEP), National Structural Code of the Philippines, 6th Edition, 2010

Introduction

PROPERTIES OF REINFORCED CONCRETE Compressive StrengthThe compressive strength of concrete is determined by testing to failure 28 day old 6-inches by 12-inches concrete cylinders at a specified rate of loading. For 28 day period the cylinders are usually kept under water or in a room with constant temperature and 100% humidity. Although concretes are available with 28-day ultimate strengths from 2500 psi (17.50 MPa) up to as high as 10,000 to 20,000 psi (70 to 140 MPa), most of the concretes used fall into the 3000 to 7000 psi (21 to 49 MPa) range.

Figure 1.1 Typical Concrete stress-strain curve, with short-term loading.

The stress-strain curves of Fig. 1.1 represent the results obtained from compression tests of sets of 28-day-old standard cylinders of varying strengths. Careful study of these curves will bring out several significant points:

a) The curves are roughly straight while the load is increased from zero to about one-third to one-half the concretes ultimate strength.b) Of particular importance is the fact that regardless of strengths, all concretes reach their ultimate strengths at strain of about 0.002.c) Concrete does not have definite yield strength; rather, the curves run smoothly on to the point of rupture at strain of from 0.003 to 0.004. It will be assumed for the purpose of future calculations in this text that concrete fails at 0.003. The reader should not that this value, which is conservative for normal-strength concretes, may not be conservative for higher-strength concretes in the 8000-psi and above range.d) Many tests have clearly shown that stress-strain curves of concrete cylinders are almost identical to those for the compression sides of beam.e) It should be further noticed that the weaker grades of concrete are less brittle than the stronger ones.

Static Modulus of Elasticity (NSCP 6th ed., page 4-39)Concrete has no clear-cut modulus of elasticity. It value varies with different concrete strengths, concrete age, type of loading, and the characteristics and proportions of the cement and aggregates.

= varying from 1500 to 2500 = Compressive strength of concrete in

Should normal crushed stone or gravel concrete with mass approximately 2320 kg/m3 be used

Concrete with strength above 6000 psi (42 MPa) are referred to as high strength concretes. Tests have indicated that the usual ACI equations for when applied to high strength concretes result in value that are too large. Based on studies at Cornell University, the expression to follow has been recommended for normal-weight concretes with values greater than 42 MPa and up to 84 MPa and for light weight concretes with greater than 42 MPa and up to 63 MPa.

Tensile Strength The tensile strength of concrete varies from about 8 to 15% of its compressive strength. A major reason for this small strength is the fact that concrete is filled with fine cracks. The tensile strength of concrete doesnt vary in direct proportion to the square root of. This strength is quite difficult to measure with direct axial tension loads because problems in gripping test specimens so as to avoid stress concentrations and because of difficulties aligning the loads. As a result of these problems, two rather indirect tests have been developed to measure concretes tensile strength. These are the modulus of rupture and the split-cylinder tests.

The tensile strength of concrete is flexure is quite important when considering beam cracks and deflections. For these considerations the tensile strength obtained with the modulus of rupture test have long been used. The modulus of rupture is usually measured by loading a 6-in x 6-in x 30-in plain rectangular beam with simple supports placed 24 in. on center) to failure with equal concentrated loads at its one-third points as per ASTM C496-96.

The stress determined in this manner is not very accurate because in using the flexure formula we are assuming the concrete is perfectly elastic, with stresses varying in direct proportion to distance from the neutral axis. These assumptions are not very good.

Based on hundreds of tests, the Code provides a modulus of rupture equal to 0.7 where is in MPa.

The tensile strength of concrete may also be measured with the split-cylinder test.

Figure 1.2 Split-cylinder test

The cylinder will split in half from end to end when its tensile strength is reached. The tensile strength at which splitting occurs is referred to as the split-cylinder strength and can be calculated with the following expression,

In which is the maximum compressive force, is the length, and is the diameter of the cylinder. The tensile strengths obtained are not very accurate.

SI BAR SIZE

Table 1.1

IDENTIFYING MARKS ON REINFORCING BARS

Figure 1.3 Identification marks for ASTM Standard bars. Chapter 01-Introduction | 6