m3l19

# m3l19 - MODULE 3 ANALYSIS OF STATICALLY INDETERMINATE...

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MODULE 3 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE DISPLACEMENT METHOD Version 2 CE IIT, Kharagpur

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LESSON 19 THE MOMENT- DISTRIBUTION METHOD: STATICALLY INDETERMINATE BEAMS WITH SUPPORT SETTLEMENTS Version 2 CE IIT, Kharagpur
Instructional Objectives After reading this chapter the student will be able to 1. Solve continuous beam with support settlements by the moment- distribution method. 2. Compute reactions at the supports. 3. Draw bending moment and shear force diagrams. 4. Draw the deflected shape of the continuous beam. 19.1 Introduction In the previous lesson, moment-distribution method was discussed in the context of statically indeterminate beams with unyielding supports. It is very well known that support may settle by unequal amount during the lifetime of the structure. Such support settlements induce fixed end moments in the beams so as to hold the end slopes of the members as zero (see Fig. 19.1). In lesson 15, an expression (equation 15.5) for beam end moments were derived by superposing the end moments developed due to 1. Externally applied loads on beams 2. Due to displacements B A θ , and Δ (settlements). The required equations are, Δ + + = AB B A AB AB F AB AB L L EI M M 3 2 2 θθ (19.1a) Version 2 CE IIT, Kharagpur

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Δ + + = AB A B AB AB F BA BA L L EI M M 3 2 2 θθ (19.1b) This may be written as, (19.2a) [] S AB B A AB F AB AB M K M M + + + = 2 2 [ ] 22 F BA BA AB B A BA S M MK M =+ + + (19.2b) where AB AB AB L EI K = is the stiffness factor for the beam AB . The coefficient 4 has been dropped since only relative values are required in calculating distribution factors. Note that 2 6 AB AB S BA S AB L EI M M Δ = = ( 1 9 . 3 ) S AB M is the beam end moments due to support settlement and is negative (clockwise) for positive support settlements (upwards). In the moment-distribution method, the support moments and due to uneven support settlements are distributed in a similar manner as the fixed end moments, which were described in details in lesson 18. S AB M S BA M It is important to follow consistent sign convention. Here counterclockwise beam end moments are taken as positive and counterclockwise chord rotation ⎛ Δ L is taken as positive. The moment-distribution method as applied to statically indeterminate beams undergoing uneven support settlements is illustrated with a few examples.
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## This note was uploaded on 06/30/2009 for the course CE 358 taught by Professor Trifunac during the Fall '07 term at USC.

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m3l19 - MODULE 3 ANALYSIS OF STATICALLY INDETERMINATE...

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