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Unformatted text preview: Lecture 4 - Page 1 of 13 Lecture 4 – Flexural Members (cont.) Determining the usable moment capacity, M u , of a rectangular reinforced concrete beam is accomplished by using the formula below: (see Lect. 3) M u = 0.9A s f y d(1 - ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ c y act f f ' 59 . ρ ) Designing a beam using the equation above is much more difficult. Assuming the material properties and dimensions are known, the equation above still has 2 unknown variables – A s and ρ act . Therefore, design of steel reinforcement for a given beam is largely one of trial-and-error. Beam Design Design of concrete beam members is often one of trial-and-error . It’s impossible to directly solve for all the variables in a reinforced concrete beam. Usually, material properties are known as well as maximum applied factored moment, M max . The following Table is useful to get a “trial” beam size: Minimum Suggested Thickness “h” of Concrete Beams & One-Way Slabs End Conditions Member: Simply supported One end continuous Both ends continuous Cantilever Solid one-way slab L/20 L/24 L/28 L/10 Beam L/16 L/18.5 L/21 L/8 Span length L = inches Beams are usually rectangular having the width typically narrower than the height. The diagram below shows typical beam aspect ratios: h L h ≈ 1.5b → 2.5b b NOTE : Beam cross-section dimensions “b” and “h” are USUALLY in multiples of 2” or 4” for ease of formwork. Lecture 4 - Page 2 of 13 Beam Design Aid It is still difficult to directly design a reinforced concrete beam even if dimensions and material properties are known. The use of design aids are commonly used to streamline the design process instead of laboriously using a trial-and-error approach. The design aid shown below is used for design or analysis. Values of 2 bd M u φ are in units of PSI. It can be used to directly solve for ρ act knowing factored actual moment M u , f’ c , f y , b and d....
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This note was uploaded on 05/01/2010 for the course CEE 615 taught by Professor Parra during the Winter '09 term at University of Michigan-Dearborn.
- Winter '09