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INTRODUCTION TO PRC II 1 CE-401 PLAIN & REINFORCED CONCRETE-II 3+0 • • • • Schedule: Tuesday and Thursday 08:00 am to 9:30 am Venue: Computer Lab-4 Objective: To give concept to students about the conventional and advanced designing approaches for various structural elements. • Course Contents • Flat Slab, Flat Plate and Waffle Slab: Analysis and design of flat plate, flat slabs and waffle slabs, for flexure and shear under gravity loading. • Slender Columns: Analysis and design of slender columns subjected to combined flexure and axial loading, Guidelines for design of shear walls-an over view. • Design of Different Types of Foundations: Analysis and design of eccentric, strap, strip and mat footings, piles and pile caps, Buoyant Footings. • Stairs: Analysis and Design of Various Types of Stairs and Staircases. 2 Pre-stressing • Principles & Design Philosophy: Principles of prestressing, properties of high strength materials, Importance of high strength concrete and steel used in pre-stressing, Behavioral aspects of pre-stressed beams and comparison with reinforced concrete beams, posttensioning and pre-tensioning techniques, Profiles of post-tensioned tendons, bonded and non-bonded tendons, comparison and hard-ware requirements. • Pre-stress Losses: Pre-stress losses, immediate and time dependent losses, lump sum and detailed estimation of pre-stress loss. • Analysis and Design: Simply supported pre-stressed beams for flexure and shear. 3 Books Recommended • Nilson, A.H., Darwin, D. and Dolan, C.W., Design of Concrete Structures Fourteenth Edition • McCormac, J.C. and Nelson, J.K., Design of Reinforced Concrete Sixth Edition • Nilson A.H., Design of Pre-stressed concrete, John Wiley and Sons. • Gregor, J.G.M. Reinforced Concrete Design, Prentice Hall 4 Weekly Course Distribution Week 01 02 Topics to be covered Overview one-way slab. Analysis and design of flat plate for flexure and shear under gravity loading. Analysis and design of flat slab for flexure and shear under gravity loading, Overview of waffle slab. 03 Introduction to columns, overview of short columns. Introduction to slender columns. 04 Analysis and design of slender columns. 05 Overview of various types of staircases. 06 Overview of shear wall design, isolated footing and rectangular footing. 07 Design of combined footing. 08 Analysis and design of strip and strap footings. 09 Comments Assignment: 01 Quiz: 01 Assignment: 01 (DD) Assignment: 02 Assignment: 02 (DD) Assignment: 03 Quiz: 02 Mid Semester Exams 5 Week Topics to be covered Comments 10 Analysis and design of eccentric, mat footings, and Assignment:03 (DD) buoyant footings. Assignment: 04 11 Overview of piles and pile caps. 12 Principles of pre-stressing, Properties of high strength materials, Importance of high strength concrete and steel Assignment:04 (DD) used in pre-stressing, behavioral aspects of pre-stressed beams and comparison with reinforced concrete beams. 13 Post tensioning and pre-tensioning techniques, profiles of Quiz: 04 post tensioned tendons, bonded and non-bonded tendons, Assignment: 05 comparison and hardware requirements. 14 Pre-stress losses, immediate and time dependent losses, lump sum and detailed estimation of pre-stress force, Quiz: 05 simply supported pre-stressed beams for flexure and shear. 15 Design of Pre Stressed Beams 16 Quiz: 03 Assignment: 05(DD) Introduction to seismic design / Revision 6 Letter Grades and Numerical Value • Letter Grade Numerical Value A AB+ B BC+ C F 4.00 3.67 3.33 3.00 2.67 2.33 2.00 0.00 7 Course Grading System Grades will be determined on the basis of • • • • • 5 Assignments 5 Quizzes Mid-term test Term Project End Semester Exam 10% 10% 20% 15% 45% 8 Rules for Class • Start with Talawat/translation • TA/Grader: Ms Siddique • Office Hours: MW 11-30 to 13-00 • All material shall be available in advance on the website/ through Group Mail [email protected] • Students are expected to come prepared for the class • Solving of home assignment in class will contribute towards the student’s grading of the course • Disclaimer / Seating Plan 9 Flat Plate/Slabs Two Way Slabs 10 TYPES OF SLABS • Gen broad flat plate, usually horizontal with top and bottom surfaces parallel or nearly so • May be supported by: – RC beams, masonry or RC walls, structural steel cols, directly by columns, or continuously by the gr • Support conditions: – – – – – Two opposite sides Beams on all four sides Intermediate beams Directly by columns Directly by columns with thick ended region near columns – Ribbed construction – On ground continuously 11 INTRODUCTION In general, slabs are classified as being one-way or two-way. Slabs that primarily deflect in one direction are referred to as one-way slabs. Simple-span, one-way slabs have previously been discussed; while the design of continuous slabs so that the slabs can deflect in two directions, referred to as two-way slabs will be discussed in detail. Depending on load conditions and other requirements slabs may be strengthened by the addition of beams between the columns, by thickening the slabs around the columns (drop panels), and by flaring the columns under the slabs (column capitals). These situations will be shown and discussed in the lecture. 12 TYPES OF SLABS 13 TYPES OF SLABS 14 TYPES OF SLABS Flat plates are solid concrete slabs of uniform depths that transfer loads directly to the supporting columns without the aid of beams or capitals or drop panels. Flat plates can be constructed quickly due to their simple formwork and reinforcing bar arrangements. They need the smallest overall story heights to provide specified headroom requirements, and they give the most flexibility in the arrangement of columns and partitions. They also provide little obstruction to light and have high fire resistance because there are few sharp corners where spalling of the concrete might occur. Flat plates are probably the most commonly used slab system today for multistory reinforced concrete hotels, motels, apartment houses, hospitals, and dormitories. 15 TYPES OF SLABS Flat plates present a possible problem in transferring the shear at the perimeter of the columns. In other words, there is a danger that the columns may punch through the slabs. As a result, it is frequently necessary to increase column sizes or slab thicknesses or to use shear heads. Shear heads consist of steel I or channel shapes placed in the slab over the columns. Although such procedures may seem expensive, it is noted that the simple formwork required for flat plates will usually result in such economical construction that the extra costs required for shear heads are more than canceled. For heavy industrial loads or long spans, however, some other type of floor system may be required. 16 TYPES OF SLABS 17 TYPES OF SLABS Flat slabs include two-way reinforced concrete slabs with capitals, drop panels, or both. These slabs are very satisfactory for heavy loads and long spans. Although the formwork is more expensive than for flat plates, flat slabs will require less concrete and reinforcing than would be required for flat plates with the same loads and spans. They are particularly economical for warehouses, parking and industrial buildings, and similar structures where exposed drop panels or capitals are acceptable. 18 TYPES OF SLABS In Figure above a two-way slab with beams is shown. This type of floor system is obviously used where its cost is less than the cost of flat plates or flat slabs. In other words, when the loads or spans or both become quite large, the slab thickness and column sizes required for flat plates or flat slabs are of such magnitude that it is more economical to use two-way slabs with beams, despite the higher formwork costs. 19 TYPES OF SLABS Another type of floor system is the waffle slab, an example of which is shown in the next slide. The floor is constructed by arranging square fiberglass or metal pans with tapered sides with spaces between them as shown. When the concrete is placed over and between the pans, the waffle shape is obtained. The intervals or gaps between the pans form the beam webs. These webs are rather deep and provide large moment arms for the reinforcing bars. With waffle slabs, the weight of the concrete is greatly reduced without significantly changing the moment resistance of the floor system. As in flat plates, shear can be a problem near columns. Consequently, waffle floors are usually made solid in those areas to increase shear resistance. Many slabs are continuously sp on the gr, as for highways, airports, warehouse floors. In such cases, a well compacted layer of crushed stone or gravel is provided to ensure uniform support and to allow for sub grade drainage. 20 TYPES OF SLABS 21 TYPES OF SLABS • Reinforced concrete slabs being discussed are usually designed for loads assumed to be uniformly distributed over the entire slab panel, bounded by beams or supporting columns centerlines. Minor concentrated loads can be accommodated through two-way action of the reinforcement. Heavy concentrated loads generally require supporting beams. • The one way and two structural action can be visualized as shown in next two slides. 22 ONE-WAY SLAB ACTION 23 TWO-WAY SLAB ACTION 24 BEHAVIOR OF TWO-WAY EDGE-SUPPORTED SLAB 25 CORNER REINFORCEMENT 26 27 TEMPERATURE AND SHRINKAGE REINFORCEMENT 28 TEMPERATURE AND SHRINKAGE REINFORCEMENT 29 TEMPERATURE AND SHRINKAGE REINFORCEMENT 30 ANALYSIS OF TWO-WAY SLABS 31 ANALYSIS OF TWO-WAY SLABS Two-way slabs bend under load into dish-shaped surfaces, so there is bending in both principal directions. As a result, they must be reinforced in both directions by layers of bars that are perpendicular to each other. A theoretical elastic analysis for such slabs is a very complex problem due to their highly indeterminate nature. Numerical techniques such as finite difference and finite elements are required, but such methods are not really practical for routine design. Actually, the fact that a great deal of stress redistribution can occur in such slabs at high loads makes it unnecessary to make designs based on theoretical analyses. Therefore the design of two-way slabs is generally based on empirical moment coefficients, which, though they might not accurately predict stress variations, result in slabs with satisfactory overall safety factors. In other words, if too much reinforcing is placed in one part of a slab and too little somewhere else, the resulting slab behavior will probably still be satisfactory. The total amount of reinforcement in a slab seems more important than its exact placement. 32 ANALYSIS OF TWO-WAY SLABS You should clearly understand that next three lectures are devoted to two-way slab design based on approximate methods of analysis, there is no intent to prevent from using more exact methods. You may design slabs on the basis of numerical solutions, yield-line analysis, or other theoretical methods, provided that it can be clearly demonstrated that they have met all the necessary safety and service ability criteria required by the ACI Code. Although it has been the practice of designers for many years to use approximate analyses for design and to use average moments rather than maximum ones, two-way slabs so designed have proved to be very satisfactory under service loads. Furthermore, they have been proved to have appreciable overload capacity. 33 DESIGN OF TWO-WAY SLABS THE ACI CODE 34 DESIGN OF TWO-WAY SLABS BY THE ACI CODE The ACI Code (13.5.1.1) specifies two approximate methods for designing two-way slabs for gravity loads. These are the equivalent frame method and the direct design method. Equivalent Frame Method In this method a portion of a structure is taken out by itself, as shown in the next figure. The same stiffness values are used for the equivalent frame method as used for the direct design method. This method, is very satisfactory for frames with unusual dimensions or loadings. 35 DESIGN OF TWO-WAY SLABS BY THE ACI CODE 36 DESIGN OF TWO-WAY SLABS ACI 318-08 Direct Design Method The Code (13.6) provides a procedure with which a set of moment coefficients can be determined. The method, in effect, involves a single-cycle moment distribution analysis of the structure based on (a) the estimated flexural stiffness's of the slabs, beams (if any), and columns and (b) the torsional stiffness's of the slabs and beams (if any) transverse to the direction in which flexural moments are being determined. These types of moment coefficients have been used satisfactorily for many years for slab design. They do not, however, give very satisfactory results for slabs with unsymmetrical dimensions and loading patterns. 37