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# Note for Structural Analysis-2 - SA-2 By Amity Kumar

• Structural Analysis-2 - SA-2
• Note
• Amity University - AMITY
• Civil Engineering
• 8 Topics
• 33326 Views
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Structural Analysis – II TABLE OF CONTENT UNIT TOPIC Unit – 1 Unit – 2 Unit – 3 Unit – 4 Unit – 5 Unit – 6 Unit – 7 Unit – 8 Rolling load and influence lines Slope deflection method Moment distribution method Sway analysis Kanis methods Flexibility matrix method of analysis Stiffness matrix method of analysis Basic principles of dynamics PAGE NO 4 14 31 43 57 67 77 86

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Structural Analysis – II For example, we can construct influence lines for (shear force at B ) or (bending moment at) or (vertical reaction at support D ) and each one will help us calculate the corresponding response parameter for different sets of loading on the beam AD (Figure 2). Figure 2 Different response parameters for beam AD An influence line is a diagram which presents the variation of a certain response parameter due to the variation of the position of a unit concentrated load along the length of the structural member. Let us consider that a unit downward concentrated force is moving from point A to point B of the beam shown in Figure 3a. We can assume it to be a wheel of unit weight moving along the length of the beam. The magnitude of the vertical support reaction at A will change depending on the location of this unit downward force. The influence line for (Figure3b) gives us the value of for different locations of the moving unit load. From the ordinate of the influence line at C, we can say that when the unit load is at point C . Figure 3b Influence line of for beam AB

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Structural Analysis – II Thus, an influence line can be defined as a curve, the ordinate to which at any abscissa gives the value of a particular response function due to a unit downward load acting at the point in the structure corresponding to the abscissa. The next section discusses how to construct influence lines using methods of equilibrium. 2 Construction of Influence Lines using Equilibrium Methods The most basic method of obtaining influence line for a specific response parameter is to solve the static equilibrium equations for various locations of the unit load. The general procedure for constructing an influence line is described below. 1. Define the positive direction of the response parameter under consideration through a free body diagram of the whole system. 2..For a particular location of the unit load, solve for the equilibrium of the whole system and if required, as in the case of an internal force, also for a part of the member to obtain the response parameter for that location of the unit load.This gives the ordinate of the influence line at that particular location of the load. 3. Repeat this process for as many locations of the unit load as required to determine the shape of the influence line for the whole length of the member. It is often helpful if we can consider a generic location (or several locations) x of the unit load. 4. Joining ordinates for different locations of the unit load throughout the length of the member, we get the influence line for that particular response parameter. The following three examples show how to construct influence lines for a support reaction, a shear force and a bending moment for the simply supported beam AB . Example 1 Draw the influence line for (vertical reaction at A ) of beam AB in Fig.1 Solution: Free body diagram of AB :