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Analysis Lecture 4

# Analysis Lecture 4 - TOPIC 4 INFLUENCE LINES FOR STATICALLY...

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CIVL2007 Theory and Design of Structures II Analytical Component (2 March 2007) page 94 TOPIC 4: INFLUENCE LINES FOR STATICALLY INDETERMINATE STRUCTURES - LECTURE NOTES - Introduction Dead loads are always fixed in magnitude and position, whereas live loads can have a variety of positions on the structure although they are fixed in magnitude. Engineering structures, particularly bridges, are frequently subjected to moving live loads such as cars and trains. Axial force, shear force and bending moment diagrams are the best descriptive methods of displaying their variation along a member (i.e. beam or frame) due to a dead or fixed load. An Influence Line (IL) best represents the variation of axial force, shear force and bending moment along a member (i.e. beam or frame) due to live or moving loads. Influence lines can also represent the variation of the reactions and deflection. “An influence line represents the variation of either the reaction, shear, moment or deflection at a specific point in a member as a concentrated force moves over the member” (Hibbeler 2002) Influence Lines therefore play an important part in the design of structures (e.g. bridges, crane rails and conveyors) where loads move across their span. They consider the problem of how to place loads on a structure in order to realise the most severe stresses.

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CIVL2007 Theory and Design of Structures II Analytical Component (2 March 2007) page 95 Sometimes we may be able to determine by inspection how to place a system of loads on a structure to realise the most severe stresses. For more complicated structures and loading conditions one may not be able to rely on common sense to determine the most severe load position and a trial- and-error solution may be required. In all cases the problem may be simplified by the use of Influence Lines which shows graphically how the changing position of loads influences quantities such as reactions, bending moments, shear forces, and deflections (Timoshenko and Young 1965). An important difference between shear and moment diagrams to Influence Lines is influence lines represent the effect of a moving (live) load at a specific point on a member whilst shear force and bending moment diagrams represent the effect of fixed loads at all points along a member The basic procedure for constructing Influence Lines for indeterminate structures is the same as that for determinate structures. For determinate structures, the Influence Lines for forces and moments consist of straight- line segments, hence, only the ordinates of a few positions of the unit load need to be evaluated. However, Influence Lines for indeterminate structures are generally curved lines or curved-line segments, hence they require calculation of many more ordinates.
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Analysis Lecture 4 - TOPIC 4 INFLUENCE LINES FOR STATICALLY...

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