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1. Calculate the 2nd moment of area for a beam with a length of 200 mm, a width of 20 mm and a height of 3 mm. 2. For the same beam, and using the provided equations, calculate the maximum deflection if the beam was cantilevered, had a Young's modulus of 207 GPa and had a load of 2.5 N applied at the free end. 6.3. Data Analysis The deflection of beams is governed by Euler-Bernoulli beam theory, for which we will consider the two experimental setups (see Figure 4). As would be expected in a cantilevered beam, the maximum deflection (max) occurs at the free end of the beam, and in the simply supported beam it occurs at the centre of the beam. To calculate the maximum deflection Equation (1) for the cantilevered and Equation (2) for the simply supported beam can be used. In both equations L is the length of the beam (mm), E is Young's modulus (MPa or N/mm²), P is the load (Newtons), and I is the 2nd moment of inertia (mm) which for a rectangular cross-section beam can be found using Equation (3). (a) (b) 8 L/2 L/2 блак Figure 4: Diagram of beam showing point of maximum deflection for (a) cantilevered beam, (b) simply supported beam PL³ 8max P (1) 3EI 3EI PL3 L3 Omax= P (2) 48E1 48EI bh³ 1 = (3) 12

1. Calculate the 2nd moment of area for a beam with a length of 200 mm, a width of 20 mm and a height of 3 mm. 2. For the same beam, and using the provided equations, calculate the maximum deflection if the beam was cantilevered, had a Young's modulus of 207 GPa and had a load of 2.5 N applied at the free end. 6.3. Data Analysis The deflection of beams is governed by Euler-Bernoulli beam theory, for which we will consider the two experimental setups (see Figure 4). As would be expected in a cantilevered beam, the maximum deflection (max) occurs at the free end of the beam, and in the simply supported beam it occurs at the centre of the beam. To calculate the maximum deflection Equation (1) for the cantilevered and Equation (2) for the simply supported beam can be used. In both equations L is the length of the beam (mm), E is Young's modulus (MPa or N/mm²), P is the load (Newtons), and I is the 2nd moment of inertia (mm) which for a rectangular cross-section beam can be found using Equation (3). (a) (b) 8 L/2 L/2 блак Figure 4: Diagram of beam showing point of maximum deflection for (a) cantilevered beam, (b) simply supported beam PL³ 8max P (1) 3EI 3EI PL3 L3 Omax= P (2) 48E1 48EI bh³ 1 = (3) 12

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 9.2.5P: The deflection curve for a cantilever beam AB (sec figure) is given by...
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1. Calculate the 2nd moment of area for a beam with a length of 200 mm, a width of 20 mm and a height of 3 mm. 2. For the same beam, and using the provided equations, calculate the maximum deflection if the beam was cantilevered, had a Young's modulus of 207 GPa and had a load of 2.5 N applied at the free end.
Transcribed Image Text:1. Calculate the 2nd moment of area for a beam with a length of 200 mm, a width of 20 mm and a height of 3 mm. 2. For the same beam, and using the provided equations, calculate the maximum deflection if the beam was cantilevered, had a Young's modulus of 207 GPa and had a load of 2.5 N applied at the free end.
6.3. Data Analysis The deflection of beams is governed by Euler-Bernoulli beam theory, for which we will consider the two experimental setups (see Figure 4). As would be expected in a cantilevered beam, the maximum deflection (max) occurs at the free end of the beam, and in the simply supported beam it occurs at the centre of the beam. To calculate the maximum deflection Equation (1) for the cantilevered and Equation (2) for the simply supported beam can be used. In both equations L is the length of the beam (mm), E is Young's modulus (MPa or N/mm²), P is the load (Newtons), and I is the 2nd moment of inertia (mm) which for a rectangular cross-section beam can be found using Equation (3). (a) (b) 8 L/2 L/2 блак Figure 4: Diagram of beam showing point of maximum deflection for (a) cantilevered beam, (b) simply supported beam PL³ 8max P (1) 3EI 3EI PL3 L3 Omax= P (2) 48E1 48EI bh³ 1 = (3) 12
Transcribed Image Text:6.3. Data Analysis The deflection of beams is governed by Euler-Bernoulli beam theory, for which we will consider the two experimental setups (see Figure 4). As would be expected in a cantilevered beam, the maximum deflection (max) occurs at the free end of the beam, and in the simply supported beam it occurs at the centre of the beam. To calculate the maximum deflection Equation (1) for the cantilevered and Equation (2) for the simply supported beam can be used. In both equations L is the length of the beam (mm), E is Young's modulus (MPa or N/mm²), P is the load (Newtons), and I is the 2nd moment of inertia (mm) which for a rectangular cross-section beam can be found using Equation (3). (a) (b) 8 L/2 L/2 блак Figure 4: Diagram of beam showing point of maximum deflection for (a) cantilevered beam, (b) simply supported beam PL³ 8max P (1) 3EI 3EI PL3 L3 Omax= P (2) 48E1 48EI bh³ 1 = (3) 12
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