3. Consider the following steel shaft (E = 30x10" psi) 0.75d w=200 lb/in. 0.75d -5 15 in.- What is the diameter d so the deflection at the middle is not larger than 0.2 mm? Use Energy Methods.
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- 1. Consider the following steel shaft (E = V A 0.75d 5 in.- 30 × 106 psi) ♥♥ w = 200 lb/in. 15 in.- 0.75d 5 in. What is the diameter d so the deflection at the middle is not larger than 0.2 mm. Use Energy MethodsFor the vertical rod as shown, find the deflection at A and the stress distribution. Use E-100 MPa and weight per unit volume equal to 0.06 N/cm3. (Hint: Introduce weight contribution to the nodal loads and solve using two elements and four elements.) Comment on the stress distribution. a) Use 2 & 4 elements with linear shape functions. b) Use 2 elements with quadratic shape functions. 1.6m C A -Area - 2500 cm² 8 Area - 1500 cm²4) Find the deflection midway between the supports. 4 kN/m 5 kN 1m 2 kN.m 2m 2m 2m 2m 5 mm E=200 GPA 20 mm 50 mm Beam Cross-Section Ra=2.61kn Rb=14.39kn Solve it by using singularity functions
- Do not give answer in image and hand writing1. Two squared and ground end springs arranged in series. Find the total deflection in mm. The springs have the following specifications. Upper spring: 16 actual coils of 40 mm diameter, Outside diameter of 230 mm. Lower spring: 8 active coils of 30 mm, Outside diameter of 185 mm. The maximum stress in either spring must not exceed 270 MPa. G = 82 GPaThe shaft in the diagram below is subjected to bending forces of 8kN at B and 5 kN at C as shown in the diagram. The shaft is supported in bearings near its ends at A and D. Calculate the maximum bending moment in the shaft. Give your answer to 2 d.p. in Nm but do not include units in your answer. e.g. 5000.00 NOT 5000N m
- Compute the torsional deflection in degrees of a 110 mm diameter, 1.4 meter long shaft subjected to a twist moment of 3 x 10⁶ N-mm. The torsional modulus of elasticity is 83,000 N/mm². a. 0.27 b. 0.31 c. 0.2 d. 0.24a) A steel 4 X 4X 0.25-inch square tube (moment of inertia I = 8.215 inª) is used as a simply supported beam. A 100-pound weight is dropped from a height of 24 inches onto the beam at mid- span. Find the maximum stress in the beam. Use E = 29 X 106 psi. 8 ft k = 200 lb/in 100 lb 8 ft b) Instead of fixed supports, the beam is supported by springs at both ends. Find the maximum stress in the beam when the 100-pound weight is dropped from a height of 24 inches (same beam properties as in part a). 24 in 100 lb 8 ft 24 in 8 ft k = 200 lb/in2. Use energy methods to find the deflection at the tip in the same direction as force F. The material properties are modulus E and shear modulus G. Note the handle has a rectangular cross-section over length b and a circular cross-section over length a. F Diameter d Cross section: txw (t>>w)
- A simply supported beam is shown in the figure. EI = 56,000 kN-m2. Using Double Integration Method determine the following: A. Determine the slope at point B. Express your answer in degrees. B. Determine the deflection at point C. Express your answer in millimeters. c. Determine the maximum deflection of the beam. Express your answer in millimeters. 30 kN 10 kN/m A VB D 3 m 1.5 m 1.5 m 6 m3. A circular solid shaft, with an radius of 20 mm and a length of 5 m and thin bearings at both ends, is subject to a point loading 1000 N in the middle. The young's modulus (E) is 200 GPa. Draw a shear force diagram (SFD) and a bending moment diagram (BMD) of this shaft. i. Compute the maximum deflection in the middle of the shaft. a) Hint: You should 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 ii. deflection. iii. cross section of the shaft. Compute the maximum shear stress due to a vertical shear force at a 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. Compute the maximum normal stress due to a bending moment at a iv. 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…A semi-elliptical leaf spring fully graduated which is made of stee; has a thickness of 10 mm, number of leaves is 6, the distance between eye to eye is 950 mm, width of spring is 65 mm and the width of the band is 140 mm. use E = 200,000 MPa and working stress of spring material as 360 MPa. Determine the deflection of the spring. Select one: O a. 73.4 mm O b. 33.3 mm O c. 57.9 mm O d. 40.6 mm