CHAPTER I REINFORCED CONCRETE 1.1. BASIC CONCEPT OF REINFORCED CONCRETE Although concrete is used very extensively in the construction of buildings, bridges and many other engineering structures, its mechanicals properties are far from ideal or not so perfect. For example, it is not a particularly or predominantly strong material. The compressive strength of structural grade concrete ranges typically or normally from 20 to 40 Mpa - 1MPa = 106 N/m² =1N/mm² = 0.10197 kgf/mm² -. MPa is a metric (SI) unit for pressure, or force per unit area. Pa is the Pascal, which is one Newton of force applied to one square meter of area (1 N/m2). MPa is a megaPascal, or one million Pascals. Since atmospheric pressure is 101 000 pA, or 101 kPa (approximately 14.7 psi), this is approximately 9 atmospheres (around 150 psi). Conversion from SI to Imperial or MKS Units Megapascal (meganewton per square meter) 1 Mpa = 145.04 lbf/sq in = 0.145 psi = 20.885 ksf = 9.32 ton/sq ft (= 10.197 kgf/cm²) (= 10 bar) = N/mm² NB: MKS unit is a metric system of units based on the metre, kilogram, and second: it forms the basis of the SI units. Units of mass There are several similar units of mass or volume called the ton: Full name Common name long ton, weight ton, "ton" (UK) gross ton Quantity Notes 2240 pounds (1016.0469088 kg) Used in countries such as United Kingdom that formerly used the Imperial system 1 short ton, net "ton" (US) ton 2000 lb Used in North America 1000 kg In UK and areas that used Imperial system, metric ton is the form of ton legal form of trade. Conveniently is less than 2% difference from long ton. ton short weight 2240 lb Used in the iron industry in the 17th century and 18th centuries. ton long weight 2400 lb Used in the iron industry in the 17th century and 18th centuries. The hundredweight was 120 lb.[1] metric ton,tonne "metric ton" CHAPTER IV FLEXURAL STRENGTH THEORY 4.1. OVERLOAD BEHAVIOUR IN FLEXURE We first consider qualitatively the behavior of a beam which after manufacture is cured for a period and is later subjected to a gradually increasing bending moment M. The beam has a rectangular section, and contains only tensile reinforcement of area Ast at depth d, as shown in figure in Fig 4.1. ε₀ d C M Tc Ast Ts Strain b Figure 4.1. Uncracked member 2 Stress Forces SOME NOTES OF SYMBOLS WRITTEN ABOVE: Ast = area of tensile steel reinforcement. b = width of a rectangular cross section; or total width of the compressive face in an I or T section. C = compressive force or column cross-section; or St. Venant torsion constant for the cross section of a beam (chapter 14). d = effective depth (depth to tensile steel) for a cross-section. M = bending moment. T = tensile force; or torsion. Tc = tensile force of concrete. Ts = tensile force of steel. ε₀ = strain at extreme compressive face of cross-section in bending or combined bending and compression. = concrete stress at extreme compressive face. SOME CONCISE THEORIES ABOUT: Strain in Mechanics is a force tending to pull or stretch something to an extreme or damaging degree. Strain or deformation is the change in shape of a body caused by an external loading In Physics is the magnitude of a deformation, equal to the change in the dimension of a deformed object divided by its original dimension. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load. If the load is small, the distortion will probably disappear when the load is removed. The intensity, or degree, of distortion is known as strain. If the distortion disappears and the metal returns to its original dimensions upon removal of the load, the strain is called elastic strain. If the distortion disappears and the metal remains distorted, the strain type is called plastic strain. Stress is the internal resistance, or counterforce, of a material to the distorting effects of an external force or load. These counter forces tend to return the atoms to their normal positions. The total resistance developed is equal to the external load. This resistance is known as stress. GOOGLE SEARCH Compressive and Tensile Force 1. Basic Types of Stresses, Tensile Stress, Compressive Stress and Shear Stress. http://www.eduresourcecollection.com/civil_sm_Stresses.php [Online] (Accessed on 22/02/09) 3 Strength of Materials – Stress Stresses Stress is defined as the internal resistance set up by a body when it is deformed. It is measured in N/m2 and this unit is specifically called Pascal (Pa). A bigger unit of stress is the mega Pascal (MPa). 1 Pa = 1N/m2, 1MPa = 106 N/m2 =1N/mm2. Three Basic Types of Stresses Basically three different types of stresses can be identified. These are related to the nature of the deforming force applied on the body. That is, whether they are tensile, compressive or shearing. Tensile Stress Consider a uniform bar of cross sectional area A subjected to an axial tensile force P. The stress at any section x-x normal to the line of action of the tensile force P is specifically called tensile stress pt. Since internal resistance R at x-x is equal to the applied force P, we have, pt = (internal resistance at x-x) / (resisting area at x-x) =R/A=P/A. Under tensile stress the bar suffers stretching or elongation. Compressive Stress If the bar is subjected to axial compression instead of axial tension, the stress developed at x-x is specifically called compressive stress pc. pc =R/A = P/A. 4 Under compressive stress the bar suffers shortening. Shear Stress Consider the section x-x of the rivet forming joint between two plates subjected to a tensile force P as shown in figure. The stresses set up at the section x-x acts along the surface of the section, that is, along a direction tangential to the section. It is specifically called shear or tangential stress at the section and is denoted by q. q =R/A =P/A. Normal or Direct Stresses When the stress acts at a section or normal to the plane of the section, it is called a normal stress or a direct stress. It is a term used to mean both the tensile stress and the compressive stress. Simple and Pure Stresses The three basic types of stresses are tensile, compressive and shear stresses. The stress developed in a body is said to be simple tension, simple compression and simple shear when the stress induced in the body is (a) single and (b) uniform. If the condition (a) alone is satisfied, the stress is called pure tension or pure compression or pure shear, as the case may be. Volumetric Stress Three mutually perpendicular like direct stresses of same intensity produced in a body constitute a volumetric stress. For example consider a body in the shape of a cube subjected equal normal pushes on all its six faces. It is now subjected to equal compressive stresses p in all the three mutually perpendicular directions. The body is now said to be subjected to a volumetric compressive stress p. 5 Volumetric stress produces a change in volume of the body without producing any distortion to the shape of the body. GOOGLE SEARCH Solved Problem about Reinforced Concrete 2. Schaum's Outline of Theory and Problems of Reinforced Concrete Design - Google Books Result. http://books.google.com.au/books?id=UAakcDL2658C&pg=P A102&lpg=PA102&dq=Solved+Problem+about+reinforced+co ncrete&source=bl&ots=pyA1usNOfb&sig=gazSasXXOQQNNW rCtVDqMKQqGc&hl=en&ei=4jiiSZTmOoGStQPvrY3NCQ&sa=X&oi= book_result&resnum=1&ct=result [Online] Accessed on 23/02/09 As the concrete hardens, it shrinks. The steel reinforcement bounded or encircled to the concrete is subjected to a gradually increasing compressive force equilibrated by concrete stresses which are mainly tensile. The fibers in the upper or higher portion of the beam shorten more than those adjacent to or next to the steel and the resulting strain gradient or raised produce a downward deflection of the member prior to or before the application of any external load. This shrinkage or contraction warping i.e. bending out of shape can be of practical significance if the member is slender or small; however, the shrinkage stresses are usually ignored in the analysis and design of normal flexural or bent members. They are not shown in figure 4.1. 6 u C k’d Mu l’ T st Forces Strain fsy Stress What is the definition of compressive force C? A compressive force C is a force or pressure that attempts or seeks to flatten or squeeze a material pushing at both ends. What is the definition of tensile force T? A tensile force T is a stretching force (tension) pulling at both ends of a component or structure along its length. At all stages/phases of loading the basic equilibrium requirements are that the resultant compressive force C and tensile force T are equal in magnitude. C=T ULTIMATE MOMENT CALCULATION Calculate the moment carrying capacity of a rectangular section, containing only tensile reinforcement, with the following properties: Fc’ = 30 Mpa Fsy = 230 Mpa b = 250 d = 350 7 Ast = 1800 mm SOLUTION: (a) Lever arm: l’ = (c) Ultimate Moment = Mu Here the resultant tensile forces in the concrete and steel, Tc and Ts, are together equal to the resultant compressive force C, and these forces form an internal couple equal to moment M so we have an external applied moment formula as follow The formula of applied Ultimate Moment: Mu = T x l’ Mu = 414 x 317 = 1.31 x 10 exp.8 Nmm = 131,000,000Nmm 131,000,000Nmm to be reduced to kNm is equal to 131,000,000Nmm 10 exp.3 x 1 meter x 1000 = 131 kNm Question Sir, please let me know the approximate total load (DL+LL) for a typical common 2-storey family house of 100 m2 (e.g. .... KN/m2) Answer This will vary between 14-18 kN/m2 per floor for habitable spaces and about 12-14 kN/m2 for the roof, assuming all construction is in stone/block work and reinforced concrete. So overall, for a 2-storey building plus roof, it will be a maximum of 18+18+14 = 50 kN/m2 time 100 equals 5000 kN or about 500 tonnes. 1. Structural Software Inc. Beam Strength http://www.strucsoft.com/applets/BeamStrength.htm [Online] (Accessed on 21/02/09) 2. reinforced concrete: Definition from Answers.com 8 http://www.answers.com/topic/reinforced-concrete [Online] (Accessed on 21/02/09) <http://www.ilpi.com/msds/ref/pressureunits.html> 9 [Online] Safety Emporium for all your lab and safety needs Search PPE MSDS Topics Glossary Index Free Sites FAQ's Books Forum Prostration Regulations Glossary Software Suppliers Poll Fun stuff Understand your MSDS with the MSDemystifier Quiz Store Search ALL our MSDS info Pressure Unit Conversions Definition Pressure is a measure of the force against a surface. Pressure is usually expressed as a force per unit area. Here is a handy conversion calculator for some common pressure terms. The definitions of each term are in the following section. Pressure Conversion Calculator (Enter number on the left side; answer appears on the right side) 10 These powered airpurifying resirators (PAPR's) are perfect for preventing infection by This many: megapascals 1 Equals torr 1.333224e-7 TB, SARS, influenza etc. Get yours at Safety Emporium Additional Info Many of the items you will find on an MSDS come in both English (U.S. Customary System) and metric (International System or SI or cgs) units. The metric system has been adopted by almost every country except the United States. Even in the U.S., scientists and technical people use the metric system because of its ease of use. If you are unfamiliar with the terms used in these definitions, see our mass unit and distance unit conversion pages. Unit Pounds per square inch (psi, PSI, lb/in2, lb/sq in) Equivalent measurements, comments Commonly used in the U.S., but not elsewhere. Normal atmospheric pressure is 14.7 psi, which means that a column of air one square inch in area rising from the Earth's atmosphere to space weighs 14.7 pounds. Atmosphere Normal atmospheric pressure is defined as 1 atmosphere. (atm) 1 atm = 14.6956 psi = 760 torr. Torr (torr) Based on the original Torricelli barometer design, one atmosphere of pressure will force the column of mercury (Hg) in a mercury barometer to a height of 760 millimeters. A pressure that causes the Hg column to rise 1 millimeter is called a torr (you may still see the term 1 mm Hg used; this has been replaced by the torr. "mm Hg" is commonly used for blood pressure measurements). 1 atm = 760 torr = 14.7 psi. Bar (bar) The bar nearly identical to the atmosphere unit. One bar = 750.062 torr = 0.9869 atm = 100,000 Pa. There are 1,000 millibar in one bar. This unit is used by meteorologists who find it easier to refer to atmospheric Millibar (mb or mbar) pressures without using decimals. One millibar = 0.001 bar = 0.750 torr = 100 Pa. Pascal (Pa) Kilopascal 1 pascal = a force of 1 Newton per square meter (1 Newton = the force required to accelerate 1 kilogram one meter per second per second = 1 kg.m/s2; this is actually quite logical for physicists and engineers, honest). 1 pascal = 10 dyne/cm2 = 0.01 mbar. 1 atm = 101,325 Pascals = 760 mm Hg = 760 torr = 14.7 psi. The prefix "kilo" means "1,000", so one kilopascal = 11 (kPa) 1,000 Pa. Therefore, 101.325 kPa = 1 atm = 760 torr and 100 kPa = 1 bar = 750 torr. The prefix "mega" means "1,000,000", so one Megapascal megapascal = 1,000 kPa = 1,000,000 Pa = 9.869 atm = (MPa) 145 psi. Gigapascal (GPa) The prefix "giga" means "1,000,000,000", so one gigapascal = 1,000 MPa = 1,000,000 kPa = 1,000,000,000 Pa = 9,870 atm = 10,000 bar. Pressures of several gigapascals can convert graphite to diamond or make hydrogen a metallic conductor! Such high pressures are rarely encountered in everyday life. MSDS Relevance Be very careful to note the units when reading numbers on an MSDS. If you ever perform a calculation of any sort, always remember to write the units next to each number in your calculation and make sure that they cancel properly. Further Reading o o The U.S. Metric Program at the National Institute of Standards. More info about the metric system, including prefixes, at ChemTeam. See also: area units, distance units, mass units, energy units, mole, temperature units, vapor pressure, volume units. Entry last updated: Wednesday, March 19, 2008. This page is copyright 2000-2008 by ILPI. Unauthorized duplication or posting on other web sites is expressly prohibited. Send suggestions, comments, and new entry desires (include the URL if applicable) to us by email. Disclaimer: The information contained herein is believed to be true and accurate, however ILPI makes no guarantees concerning the veracity of any statement. 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