lecture9 - Lecture 9 - Flexure June 20, 2003 CVEN 444...

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Unformatted text preview: Lecture 9 - Flexure June 20, 2003 CVEN 444 Lecture Goals Lecture Goals Load Envelopes Resistance Factors and Loads Design of Singly Reinforced Rectangular Beam Unknown section dimensions Known section dimensions Moment Moment Envelopes Envelopes Fig. 10-10; MacGregor (1997) The moment envelope curve defines the extreme boundary values of bending moment along the beam due to critical placements of design live loading. Moment Moment Envelopes Example Envelopes Example Given following beam with a dead load of 1 k/ft and live load 2 k/ft obtain the shear and bending moment envelopes Moment Moment Envelopes Example Envelopes Example Use a series of shear and bending moment diagrams W u = 1.2w D + 1.6w L 1 2 3 4 5 5 10 15 20 25 30 35 40 (ft) kips-80-60-40-20 20 40 60 80 5 10 15 20 25 30 35 40 ft kips-250-200-150-100-50 50 100 150 5 10 15 20 25 30 35 40 ft k-ft Shear Diagram Moment Diagram Moment Moment Envelopes Example Envelopes Example Use a series of shear and bending moment diagrams W u = 1.2w D + 1.6w L Shear Diagram Moment Diagram 0.2 0.4 0.6 0.8 1 1.2 1.4 5 10 15 20 25 30 35 40 ft k/ft-20-15-10-5 5 10 15 20 5 10 15 20 25 30 35 40 ft kips-80-60-40-20 20 40 5 10 15 20 25 30 35 40 ft k-ft (Dead Load Only) Moment Moment Envelopes Example Envelopes Example Use a series of shear and bending moment diagrams W u = 1.2w D + 1.6w L Shear Diagram Moment Diagram 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5 10 15 20 25 30 35 40 ft k/ft-60-50-40-30-20-10 10 20 30 40 50 5 10 15 20 25 30 35 40 ft kips-200-150-100-50 50 100 150 200 5 10 15 20 25 30 35 40 ft k-ft Moment Moment Envelopes Example Envelopes Example The shear envelope Moment Moment Envelopes Example Envelopes Example The moment envelope Moment Envelope-300-200-100 100 200 5 10 15 20 25 30 35 40 ft k-ft Minimum Moment Maximum Moment Flexural Design of Reinforced Flexural Design of Reinforced Concrete Beams and Slab Sections Concrete Beams and Slab Sections Analysis Versus Design : Analysis : Given a cross-section, f c , reinforcement sizes, location, f y compute resistance or capacity Design: Given factored load effect (such as M u ) select suitable section(dimensions, f c , f y , reinforcement, etc.) Flexural Design of Reinforced Flexural Design of Reinforced Concrete Beams and Slab Sections Concrete Beams and Slab Sections ACI Code Requirements for Strength Design Basic Equation : factored resistance factored load effect Ex ....
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This note was uploaded on 10/03/2011 for the course CVEN 444 taught by Professor Staff during the Summer '08 term at Texas A&M.

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lecture9 - Lecture 9 - Flexure June 20, 2003 CVEN 444...

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