2009+16-1Design - Introduction to Solid Mechanics-Vm211...

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1 SJTU Introduction to Solid Mechanics-Vm211 Chapter 16 DESIGN OF BEAMS Chapter 16 Design of Beams SJTU Introduction to Solid Mechanics-Vm211 CHAPTER OUTLINE 1. Basic for Beam Design 2. Stress Variations throughout a Prismatic Beam 3. Prismatic Beam Design 4. The Elastic Curve 5. Slope and Displacement by Integration 6. Method of Superposition 7. Statically Indeterminate Beams 8. Statically Indeterminate Beams- Method of Superposition SJTU Introduction to Solid Mechanics-Vm211 16.1 Basic for Beam Design Basis of beam design Reliability Reliability Safety : Strength concern (i.e. provide safety margin to normal/shear stress limit) Serviceability : (such as deflection limit) Durability SJTU Introduction to Solid Mechanics-Vm211 16.2 Stress Variations throughout a Prismatic Beam Fig. 11-2 σ τ SJTU Introduction to Solid Mechanics-Vm211 16.3 Prismatic Beam Design • Section strength requirement S req’d = M σ allow I Mc = σ c I S = M S = S Section Modulus SJTU Introduction to Solid Mechanics-Vm211 16.3 Prismatic Beam Design ± Choices of section: - Steel sections e.g. AISC standard (American Institute of Steel Construction) W 460 X 68 (height = 459 460mm, weight = 0.68 kN/m)
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2 SJTU Introduction to Solid Mechanics-Vm211 16.3 Prismatic Beam Design - Wood sections Nominal dimensions (in multiple of 25mm) e.g. 50 (mm) x 100 (mm) actual or “dressed” dimensions are smaller, e.g. 50 x 100 is 38 x 89. - Built-up sections SJTU Introduction to Solid Mechanics-Vm211 Procedures: - Shear and Moment Diagram - Determine the maximum shear and moment in the beam. Often this is done by constructing the beam’s shear and moment diagrams. - For built-up beams, shear and moment diagrams are useful for identifying regions where the shear and moment are excessively large and may require additional structural reinforcement or fasteners. 16.3 Prismatic Beam Design SJTU Introduction to Solid Mechanics-Vm211 Procedures: -N o r m a l S t r e s s - If the beam is relatively long , it is designed by finding its section modulus using the flexure formula, S req’d = M max / σ allow . - Once S req’d is determined, the cross-sectional dimensions for simple shapes can then be computed, using S req’d = I/c. 16.3 Prismatic Beam Design - If rolled-steel sections are to be used, several possible values of S may be selected from the Tables . Of these, choose the one having the smallest cross-sectional area, since this beam has the least weight and is therefore the most economical. - Make sure that the selected section modulus, S, is slightly greater than S req’d , so that the additional moment created by the beam’s weight is considered.
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This note was uploaded on 08/09/2011 for the course EE 211 taught by Professor Liuxila during the Summer '09 term at Shanghai Jiao Tong University.

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2009+16-1Design - Introduction to Solid Mechanics-Vm211...

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