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(a) A steel beam in the form of a cantilever of length 2 m, designed for a structural engineering application, is required to carry a load of 40 kN at the free end as shown in Figure 4(a). As the engineer implementing the design, you want to make a reasonable estimate of the vertical deflection at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm2, I= 15 x 10 mª. (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 4(b). (1) (ii) (iii) What is the main difference between the two problems from a structural analysis standpoint? To re-calculate the end deflection and the load R on the prop, using Macaulay's method, write the expression for bending moment in the entire beam and then integrate the moment equation for slope and deflection. State the boundary conditions which will lead to determination of the constants in the above expressions; the constants need not be calculated. 40 KN 2m Figure 4(a) 40 KN 1m 1m R Figure 4(b)

(a) A steel beam in the form of a cantilever of length 2 m, designed for a structural engineering application, is required to carry a load of 40 kN at the free end as shown in Figure 4(a). As the engineer implementing the design, you want to make a reasonable estimate of the vertical deflection at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm2, I= 15 x 10 mª. (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 4(b). (1) (ii) (iii) What is the main difference between the two problems from a structural analysis standpoint? To re-calculate the end deflection and the load R on the prop, using Macaulay's method, write the expression for bending moment in the entire beam and then integrate the moment equation for slope and deflection. State the boundary conditions which will lead to determination of the constants in the above expressions; the constants need not be calculated. 40 KN 2m Figure 4(a) 40 KN 1m 1m R Figure 4(b)

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter9: Deflections Of Beams
Section: Chapter Questions
Problem 9.5.4P: Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of...
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4. (a) A steel beam in the form of a cantilever of length 2 m, designed for a structural engineering application, is required to carry a load of 40 kN at the free end as shown in Figure 4(a). As the engineer implementing the design, you want to make a reasonable estimate of the vertical deflection at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm², I = 15 x 10 mª. (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 4(b). (i) (ii) (iii) What is the main difference between the two problems from a structural analysis standpoint? To re-calculate the end deflection and the load R on the prop, using Macaulay's method, write the expression for bending moment in the entire beam and then integrate the moment equation for slope and deflection. State the boundary conditions which will lead to determination of the constants in the above expressions; the constants need not be calculated. 40 KN 2m Figure 4(a) 40 KN 1m 1m R Figure 4(b) 401
Transcribed Image Text:4. (a) A steel beam in the form of a cantilever of length 2 m, designed for a structural engineering application, is required to carry a load of 40 kN at the free end as shown in Figure 4(a). As the engineer implementing the design, you want to make a reasonable estimate of the vertical deflection at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm², I = 15 x 10 mª. (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 4(b). (i) (ii) (iii) What is the main difference between the two problems from a structural analysis standpoint? To re-calculate the end deflection and the load R on the prop, using Macaulay's method, write the expression for bending moment in the entire beam and then integrate the moment equation for slope and deflection. State the boundary conditions which will lead to determination of the constants in the above expressions; the constants need not be calculated. 40 KN 2m Figure 4(a) 40 KN 1m 1m R Figure 4(b) 401
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