# flexure - Lecture9Flexure June20,2003 CVEN444 LectureGoals...

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Lecture 9 - Flexure June 20, 2003 CVEN 444

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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.

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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 0 1 2 3 4 5 0 5 10 15 20 25 30 35 40 (ft) kips -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 30 35 40 ft -250 -200 -150 -100 -50 0 50 100 150 0 5 10 15 20 25 30 35 40 ft k-ft Shear Diagram Moment Diagram

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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 0.2 0.4 0.6 0.8 1 1.2 1.4 0 5 10 15 20 25 30 35 40 ft k/ft -20 -15 -10 -5 0 5 10 15 20 0 5 10 15 20 25 30 35 40 ft kips -80 -60 -40 -20 0 20 40 0 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 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 20 25 30 35 40 ft k/ft -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 ft kips -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 30 35 40 ft k-ft

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Moment Moment Envelopes Example Envelopes Example The shear envelope
Moment Moment Envelopes Example Envelopes Example The moment envelope Moment Envelope -300 -200 -100 0 100 200 0 5 10 15 20 25 30 35 40 ft k-ft Minimum Moment Maximum Moment

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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  Concrete Beams and Slab Sections Concrete Beams and Slab Sections ACI Code Requirements for Strength Design Basic Equation : factored resistance factored load effect Ex . u

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## This note was uploaded on 12/16/2011 for the course STRUCTURAL 112 taught by Professor Colin during the Spring '11 term at Université Robert Schuman.

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flexure - Lecture9Flexure June20,2003 CVEN444 LectureGoals...

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