# Reinforced Concrete Design

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1 FALL 2013 C C Reinforced Concrete Design

2 CIVL 4135 ii

3 1 Chapter 1. Introduction 1.1. Reading Assignment Chapter 1 Sections 1.1 through 1.8 of text Introduction In the design and analysis of reinforced concrete members, you are presented with a problem unfamiliar to most of you: The mechanics of members consisting of two materials. To compound this problem, one of the materials (concrete) behaves differently in tension than in compression, and may be considered to be either elastic or inelastic, if it is not neglected entirely. Although we will encounter some peculiar aspects of behavior of concrete members, we will usually be close to a solution for most problems if we can apply the following three basic ideas: Geometry of deformation of sections will be consistent under given types of loading; i.e., moment will always cause strain to vary linearly with distance from neutral axis, etc. Mechanics of materials will allow us to relate stresses to strains. Sections will be in equilibrium: external moments will be resisted by internal moment, external axial load will be equal to the sum of internal axial forces. (Many new engineers overly impressed speed and apparent accuracy of modern structural analysis computational procedures think less about equilibrium and details). We will use some or all of these ideas in solving most of the analysis problems we will have in this course. Design of members and structures of reinforced concrete is a problem distinct from but closely related to analysis. Strictly speaking, it is almost impossible to exactly analyze a concrete structure, and to design exactly is no less difficult. Fortunately, we can make a few fundamental assumptions which make the design of reinforced concrete quite simple, if not easy.

4 A problem unique to the design of reinforced concrete structures is the need to detail each member throughout. Steel structures, in general, require only the detailed design of connections. For concrete structures, we must determine not only the area of longitudinal and lateral reinforcement required in each member, but also the way to best arrange and connect the reinforcement to insure acceptable structural performance. This procedure can be made reasonably simple, if not easy. Purpose of this course is to establish a firm understanding of behavior of reinforced concrete structures, then to develop method used in current practice and to achieve familiarity with codes and specifications governing practical design. In this course we will learn to understand the basic performance of concrete and steel as structural materials, and the behavior of reinforced concrete members and structures. If we understand the basic concepts behind code provisions for design, we will be able to: Approach the design in a more knowledgeable fashion, not like following a black box; and Understand and adapt the changes in code provisions better and faster. The overall goal is to be able to design reinforced concrete structures that are: Safe Economical Efficient Reinforced concrete is one of the principal building materials used in engineered structures because: Low cost Weathering and fire resistance Good compressive strength Formability all these criteria make concrete an attractive material for wide range of structural applications such as buildings, dams, reservoirs, tanks, etc Design Codes and Specifications Buildings must be designed and constructed according to the provisions of a building code, which is a legal document containing requirements related to such things as structural safety, fire safety, plumbing, ventilation, and accessibility to the physically disabled. A building code has CIVL 4135 Chapter 1. Introduction 2

6 Environmental Loads Environmental Loads consist of wind, earthquake, and snow loads. such as wind, earthquake, and snow loads Serviceability Serviceability requires that Deflections be adequately small; Cracks if any be kept to a tolerable limits; Vibrations be minimized. CIVL 4135 Chapter 1. Introduction 4

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9 CIVL 4135 Chapter 1. Introduction 7

15 1.13. Design Strength (Section 9.3 of the ACI Code) The strength of a particular structural unit calculated using the current established procedures is termed nominal strength. For example, in the case of a beam the resisting moment capacity of the section calculated using the equations of equilibrium and properties of concrete and steel is called the nominal moment capacity M n of the section. The purpose of the strength reduction factor f are (MacGregor, 1976; and Winter, 1979): to allow for under-strength members due to variations in material strengths and dimensions to permit for inaccuracies in the design provisions to reflect the degree of ductility and required probability of the member under the load effects being considered to reflect the importance of the member in the structure. CIVL 4135 Chapter 1. Introduction 13

16 Table 1.3. Strength Reduction Factors, F, of the ACI Code. (ACI Section 9.3) Kind of Strength Strength Reduction Factor Φ Tension controlled sections as defined in Compression controlled sections as defined in (a) Members with spiral reinforcement (b) Other members For sections in which the net tensile strain in the extreme tension steel is between the limits for compression controlled and tension controlled sections, Φ may be increased in from that for compression controlled section to 0.90 as the net tensile strain in the extreme tension steel at nominal strength increases from the compression-controlled strain limit Alternatively, when Appendix B is used, for members in which f y does not exceed 60,000 psi, with symmetrical reinforcement, and with (h-d'-d s )/h not less than 0.7, Φ may be increased linearly to 0.90 as ΦP n decreases from 0.1 fa c g to zero. For other reinforced members, Φ may be increased linearly to 0.90 as Φ P n decreases from 0.1 fa c g to Φ P n, whichever is smaller, to zero Shear and torsion Bearing on Concrete Flexure sections without axial load in pretensioned members where strand embedment is less than development length as provided in Plain Concrete CIVL 4135 Chapter 1. Introduction 14

17 1.14. Example Compute Factored load to be used in the design of a column subjected to the following load effects: 9 kips compression from dead load, 5 kips compression from roof live load, 6 kips compression from snow, 7 kips compression from accumulated rain, and 8 kips compression from wind. Assume live load is greater than 100 lb/ft 2. Solution: Condition ACI Equation (9-1) U = 1.4(D + F) U = 1.4(9) = 12.6 kips Factored Loads ACI Equation (9-2) U = 1.2(D + F + T) + 1.6(L + H) + 0.5(L r or S or R) U = 1.2D + 1.6L + 0.5R U = 1.2(9) + 1.6(0) + 0.5(7) U = 14.3 kips ACI Equation (9-3) U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.8W) U = 1.2(D) + 1.6(R) + 0.8W U = 1.2(9) + 1.6(7) + 0.8(8) U = 28.4 kips ACI Equation (9-4) U = 1.2D + 1.6W + 1.0L + 0.5(L r or S or R) U = 1.2D + 1.6W + 0.5L + 0.5R U = 1.2(9) + 1.6(8) + 0.5(0) + 0.5(7) U = 27.1 kips ACI Equation (9-5) U = 1.2D + 1.0E + 1.0L + 0.2S U = 1.2(9) + 0.2(6) U = 12 kips ACI Equation (9-6) U = 0.9D + 1.6W + 1.6H U = 0.9(9) + 1.6(8) U = 20.9 kips ACI Equation (9-7) U= = 0.9D + 1.0E + 1.6H U = 0.9(9) U = 8.1 kips Therefore, U = 28.4 kips controls. CIVL 4135 Chapter 1. Introduction 15

18 1.15. Ultimate Strength vs. Working Stress Design For D and L only Working stress design 1.2D+ 1.6 L φr or 1.4D φr...(1.6) n 1.67D+ 1.67L Rn...(1.7) n Assume a strength reduction factor of φ = 0.9, Equation (1.7) becomes: 1.5D+ 1.5L 0.9R n...(1.8) Therefore, the ratio for Ultimate Strength Equation (1.6) to Working Stress Equation (1.8) becomes 1.2D+ 1.6 L or 1.4D Ratio = 1.5D+ 1.5L ( L/ D) or 1.4 Ratio = ( L/ D)... (1.9)... (1.10) CIVL 4135 Chapter 1. Introduction 16

19 1.16. References MacGregor, J.G. (1976). Safety and Limit States Design for Reinforced Concrete. Canadian Journal of Civil Engineering, 3(4), December, pp Winter, G. (1979). Safety and Serviceability Provisions in the ACI Building Code. Concrete Design: U.S. and European Practices, SP-59, American Concrete Institute, Detroit, 1979, pp Nawy, E.G.. (2003). Reinforced Concrete A Fundamental Approach. Fifth Edition, Prentice Hall. CIVL 4135 Chapter 1. Introduction 17

20 Homework Set 1 Draw the shear and moment diagrams for the beams shown below. 10 kips 10 kips 20 kips 10 kips 10 kips (A) (B) w = 1.5 k/ft 20 kips 20-9 (C) w = 2.5 k/ft kips 50 kips (D) w = 1.0 k/ft CIVL 4135 Chapter 1. Introduction 18

21 Homework Set 1 - Continued E. The reinforced concrete bridge pier shown below supports a three-girder structural steel highway bridge. Two loading cases are shown below. For each loading condition, draw the shear and moment diagrams for the beam. Determine the moment for which the beam must be designed. Determine the moment for which the column must be designed. P D + P L P D + P L P D + P L Load case 1 P D = 36 kips P L = 40 kips P D P D + P L P D + P L Load case CIVL 4135 Chapter 1. Introduction 19

22 Homework Set 1 - Continued F. A weightless cantilever supports a concentrated service load of magnitude P as shown below. The beam is a reinforced concrete having both flexure and transverse steel. Denote the theoretical shear and moment strength of the beam as V n and M n. Reliable strengths are obtained by the appropriate factors, φ, respectively. Fictitious values for these factors are given below. Factors Shear Flexure φ If the live load factor is 1.7, and the theoretical flexure and shear capacity are 110 kip-ft and 11 kip, what magnitude of P would be permitted using strength design? 11 9 Answer: P =? CIVL 4135 Chapter 1. Introduction 20

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