m7l39

m7l39 - Module 7 Influence Lines Version 2 CE IIT,...

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Module 7 Influence Lines Version 2 CE IIT, Kharagpur
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Lesson 39 Influence Lines for Beams (Contd.) Version 2 CE IIT, Kharagpur
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Instructional Objectives: The objectives of the present lesson are as follows. Construction of influence line for maximum shear at sections in a beam supporting two concentrated loads Construction of influence line for maximum moment at sections in a beam supporting two concentrated loads Construction of influence line for maximum end shear in a beam supporting a series of moving concentrated loads Construction of influence line for maximum shear at a section in a beam supporting a series of moving concentrated loads Construction of influence line for maximum moment at a section in a beam supporting a series of moving concentrated loads Construction of influence line for absolute maximum moment in s beam supporting a series of moving concentrated loads Understanding about the envelopes of maximum influence line values 39.1 Introduction In the previous lessons, we have studied about construction of influence line for the either single concentrated load or uniformly distributed loads. In the present lesson, we will study in depth about the beams, which are loaded with a series of two or more then two concentrated loads. 39.2 Maximum shear at sections in a beam supporting two concentrated loads Let us assume that instead of one single point load, there are two point loads P 1 and P 2 spaced at y moving from left to right on the beam as shown in Figure 39.1. We are interested to find maximum shear force in the beam at given section C. In the present case, we assume that P 2 <P 1 . Figure 39.1: Beam loaded with two concentrated point loads Version 2 CE IIT, Kharagpur
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Now there are three possibilities due to load spacing. They are: x<y, x=y and x>y. Case 1: x<y This case indicates that when load P 2 will be between A and C then load P 1 will not be on the beam. In that case, maximum negative shear at section C can be given by l x P V C 2 = and maximum positive shear at section C will be l x l P V C ) ( 2 = Case 2: x=y In this case, load P 1 will be on support A and P 2 will be on section C. Maximum negative shear can be given by l x P V C 2 = and maximum positive shear at section C will be l x l P V C ) ( 2 = Case 3: x>y With reference to Figure 39.2, maximum negative shear force can be obtained when load P 2 will be on section C. The maximum negative shear force is expressed as: Version 2 CE IIT, Kharagpur
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Figure 39.2: Influence line for shear at section C = l y x P l x P V C 1 2 1 And with reference to Figure 39.2, maximum positive shear force can be obtained when load P 1 will be on section C. The maximum positive shear force is expressed as: + = l y x l P l x P V C 2 1 2 From above discussed two values of shear force at section, select the maximum negative shear value. 39.3 Maximum moment at sections in a beam supporting two
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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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m7l39 - Module 7 Influence Lines Version 2 CE IIT,...

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