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Consider a three-span continuous beam ABCD, with fixed supports A & D at both ends and two interior roller supports B & C. Span AB is 3.5 meters long, BC is 4.2 meters long, and CD is 2.8 meters long. The modulus of elasticity of the beam is 200 GPa and the moment of inertia of the beam section is 400 x 100 mm. No support settlements occur at the interior supports. The said beam is to be analyzed considering live loads, with a uniform live load of 30 kN/m, while taking account pattern loadings. Pattern loadings are used to determine the maximum responses (e.g. reactions, shear, bending moments) at a certain point of the beam due to live loads. There are three types of pattern loadings: • Full Span Loading - live load is applied on all spans simultaneously; . Alternate Span Loading - live load is applied on alternate spans; and • Adjacent Span Loading-live load is applied on two adjacent spans, then skipping the next span. In the case of this problem, the following pattern loading cases should be considered: . full span loading alternate span loading (AB & CD only, BC only) adjacent span loading (AB & BC only, BC & CD only)

Consider a three-span continuous beam ABCD, with fixed supports A & D at both ends and two interior roller supports B & C. Span AB is 3.5 meters long, BC is 4.2 meters long, and CD is 2.8 meters long. The modulus of elasticity of the beam is 200 GPa and the moment of inertia of the beam section is 400 x 100 mm. No support settlements occur at the interior supports. The said beam is to be analyzed considering live loads, with a uniform live load of 30 kN/m, while taking account pattern loadings. Pattern loadings are used to determine the maximum responses (e.g. reactions, shear, bending moments) at a certain point of the beam due to live loads. There are three types of pattern loadings: • Full Span Loading - live load is applied on all spans simultaneously; . Alternate Span Loading - live load is applied on alternate spans; and • Adjacent Span Loading-live load is applied on two adjacent spans, then skipping the next span. In the case of this problem, the following pattern loading cases should be considered: . full span loading alternate span loading (AB & CD only, BC only) adjacent span loading (AB & BC only, BC & CD only)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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SITUATION 2 (Pattern Loadings on a Continuous Beam Using Three-Moment Equation) Consider a three-span continuous beam ABCD, with fixed supports A & D at both ends and two interior roller supports B & C. Span AB is 3.5 meters long, BC is 4.2 meters long, and CD is 2.8 meters long. The modulus of elasticity of the beam is 200 GPa and the moment of inertia of the beam section is 400 x 10 mm. No support settlements occur at the interior supports. The said beam is to be analyzed considering live loads, with a uniform live load of 30 kN/m, while taking account pattern loadings. Pattern loadings are used to determine the maximum responses (e.g. reactions, shear, bending moments) at a certain point of the beam due to live loads. There are three types of pattern loadings: Full Span Loading - live load is applied on all spans simultaneously; Alternate Span Loading-live load is applied on alternate spans; and Adjacent Span Loading - live load is applied on two adjacent spans, then skipping the next span. In the case of this problem, the following pattern loading cases should be considered: • full span loading . . Guide Questions: Use three-moment equation to write the systems of equations needed to solve for the bending moments acting on the beam for each pattern loading case. Express them in matrix form. . alternate span loading (AB & CD only, BC only) adjacent span loading (AB & BC only, BC & CD only) . Solve for the bending moments acting at the supports, utilizing the derived equations from the three-moment equation. Use numerical methods to solve the systems of equations. Use a tolerance approximate error of 0.05%. Compare answers solved using: O LU decomposition (Doolittle's or Crout's decomposition): O Gauss-Seidel iteration method; and O Gauss-Seidel method with successive relaxation (Use different values of w.) Draw the shear and bending moment diagrams of the beam considering different pattern loading cases. Make a comparative analysis of these diagrams and explain their implications on the analysis and design of the said beam.
Transcribed Image Text:SITUATION 2 (Pattern Loadings on a Continuous Beam Using Three-Moment Equation) Consider a three-span continuous beam ABCD, with fixed supports A & D at both ends and two interior roller supports B & C. Span AB is 3.5 meters long, BC is 4.2 meters long, and CD is 2.8 meters long. The modulus of elasticity of the beam is 200 GPa and the moment of inertia of the beam section is 400 x 10 mm. No support settlements occur at the interior supports. The said beam is to be analyzed considering live loads, with a uniform live load of 30 kN/m, while taking account pattern loadings. Pattern loadings are used to determine the maximum responses (e.g. reactions, shear, bending moments) at a certain point of the beam due to live loads. There are three types of pattern loadings: Full Span Loading - live load is applied on all spans simultaneously; Alternate Span Loading-live load is applied on alternate spans; and Adjacent Span Loading - live load is applied on two adjacent spans, then skipping the next span. In the case of this problem, the following pattern loading cases should be considered: • full span loading . . Guide Questions: Use three-moment equation to write the systems of equations needed to solve for the bending moments acting on the beam for each pattern loading case. Express them in matrix form. . alternate span loading (AB & CD only, BC only) adjacent span loading (AB & BC only, BC & CD only) . Solve for the bending moments acting at the supports, utilizing the derived equations from the three-moment equation. Use numerical methods to solve the systems of equations. Use a tolerance approximate error of 0.05%. Compare answers solved using: O LU decomposition (Doolittle's or Crout's decomposition): O Gauss-Seidel iteration method; and O Gauss-Seidel method with successive relaxation (Use different values of w.) Draw the shear and bending moment diagrams of the beam considering different pattern loading cases. Make a comparative analysis of these diagrams and explain their implications on the analysis and design of the said beam.
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