Structural mechanics virtual work in structures with bending and axiel deformations You are given the structure and loading below. The load w is 2.4 kips/ft. Find the value of downward deflection at point D. Use E =29,000 ksi. BC is a cable with a diameter of 0.5 in. AB is an I beam (W12x16) with a moment of inertia of 103 in4 and an area of 4.7in?.12'AB12'Apply the 4-step process:1. Calculate the axial forces and bending moments for the applied load. This requires a full solution of the structure by themethods of Unit 4.2. Apply the unit load at the location of and in the direction of the desired displacement.3. Calculate the axial forces and bending moments for the virtual load. This requires another full solution of the structure by themethods of Unit 4.4. Compute the deflection using the equation above.Here are a few approximate partial answers to check your work along the way:• Peak real moment: 518 kip-in• Real axial force in the cable: 20.4 kipsKeep track of the three different contributions for the deflection at point D (axial and bending as appropriate)...1What is the magnitude of the deflection at D attributable to axial deformation of member BC (in inches to three decimal points)?Type your answer.2What is the magnitude of the deflection at Dattributable to axial deformation of member AB (in inches to three decimal points)?Type your answer.3What is the magnitude of the deflection at D attributable to flexure of member AB (in inches to three decimal points)?Type your answer... In this unit, we continue to expand the concept of virtual work to structures with both axial and flexural deformations. The same 4-step process still applies.1. Compute real member axial forces and bending moments2. Apply virtual load at the location of and in the direction of the desired displacement3. Compute virtual member axial forces and bending moments4. Compute the displacement according to the sum below (using tabular calculations - a spreadsheet is recommended toautomate your calculations)If we have Nm total members, we include the virtual energy stored in each member flexurally and axially:mị Mi dxA = Li=1+EA;EIAll the terms have been defined in the previous sections. An important consideration is that often in hand calculations we neglectaxial deformation in members that are subjected to both axial and flexural forces. If the problem does not give you EA for amember, you may treat it as axially rigid (infinite EA, no contribution to deflection).In this unit, you will explore this concept with the following activities:

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You are given the structure and loading below. The load w is 2.4 kips/ft. Find the value of downward deflection at point D. Use E = 29,000 ksi. BC is a cable with a diameter of 0.5 in. AB is an I beam (W12x16) with a moment of inertia of 103 inª and an area of 4.7 in². ㅏ A 12' 12' Apply the 4-step process: 1. Calculate the axial forces and bending moments for the applied load. This requires a full solution of the structure by the methods of Unit 4. 2. Apply the unit load at the location of and in the direction of the desired displacement.

You are given the structure and loading below. The load w is 2.4 kips/ft. Find the value of downward deflection at point D. Use E = 29,000 ksi. BC is a cable with a diameter of 0.5 in. AB is an I beam (W12x16) with a moment of inertia of 103 inª and an area of 4.7 in². ㅏ A 12' 12' Apply the 4-step process: 1. Calculate the axial forces and bending moments for the applied load. This requires a full solution of the structure by the methods of Unit 4. 2. Apply the unit load at the location of and in the direction of the desired displacement.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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