**Problem Description:**A circular solid shaft, with a radius of 20 mm and a length of 5 m, and supported by thin bearings at both ends, is subject to a point load of 1000 N in the middle. The Young's modulus (E) is 200 GPa.**Tasks:**i. **Draw a Shear Force Diagram (SFD) and a Bending Moment Diagram (BMD) of this shaft.**ii. **Compute the maximum deflection in the middle of the shaft.** a) **Hint:** Compute I (the second moment of inertia of the cross-section of the shaft) prior to determining the deflection. b) **Hint:** Use the table shown in the lecture note for calculating the deflection.iii. **Compute the maximum shear stress due to a vertical shear force at a cross-section of the shaft.** **Hint:** Use the formula to compute the shear stress. The maximum shear stress occurs at the neutral axis of the cross-section of a shaft.iv. **Compute the maximum normal stress due to a bending moment at a cross-section of the shaft.** **Hint:** Use the formula to compute the normal stress. The maximum normal stress occurs at the top or bottom of the cross-section of a shaft.**Visual Description:**- The shaft is shown with a point load P = 1000 N applied at its center.- The shaft length is marked as 5 m.- The radius of the shaft is given as 20 mm.- Reactions \( R_A \) and \( R_B \) are indicated at the supports at both ends. This setup provides a clear starting point for mechanical analysis of the shaft under the given conditions.

Answered: A circular solid shaft, with an radius…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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8. A solid aluminum cantilever beam is 40 cm in length and has a circular cross section with a diameter of 3.0 cm. Calculate the torsional stiffness of the beam, k,, in N-m/rad and the angular displacement at the end in deg when it is subjected to a moment of 20 N-m. 40 20 Cross-section 3.0
a) the value of the maximum bending moment in the beam. Enter your answer in kNm to three decimal places. b) the maximum normal stress in the cross-section of the beam. Enter the positive value of the stress. Enter your answer in MPa to two decimal places.
At a machined shaft shoulder the small diameter d is 1.100 in, the large diameter D is r 1.65 in, and the fillet radius is 0.11 in. The bending moment is 1260 lbf in and the steady torsion moment is 1100 lbf in. . *Hint: Refer to Table A-15's to obtain the stress concentration factors, K and Kts a) What is the maximum bending stress in the shaft? b) What is the maximum shear stress in the shaft? Q Search
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A simply supported beam with a length of 4m is loaded with a uniform distributed load (w). The beam has a rectangular hollow section with the following dimensions: Outer Base = 150 mm OuterDepth 200 mm Inner Base = 100 mm Depth = 150 mm Inner Determine the maximum uniformly distributed load which can be applied over the entire length of the beam if the bending stress is limited to 8 Mpa. Please answer with solution and fbd. Thank you.
(a) For the cantilever beam shown in Figure Q1, 60 N 40 N/m 80 Nm 1m 1m 1m 1m Figure Q1 (i) write bending moment expression, M(x), using the Macauley's method determine the bending moment using M(x) for specified (ii) cross-sections at E, C and A (iii) justify the bending moment result calculated in (ii) for the free end of the beam at A (b) For a rectangular cross-section of width 100 mm and height 400 mm of a beam, the shear force is 2x106 N. Calculate the shear stress (t) at the following locations: (i) (ii) The top surface (iii) 60 mm from the top surface The neutral axis
Prob # 3. Find the torsional deflection of a solid steel shaft 100 mm in diameter and 130 mm long subjected to twisting moment of 3 x 106 N-mm. The torsional modulus of elasticity is 80,000 N/mm2. a. 122 deg b. 285 deg c. 0.234 deg d. 0.543 deg
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