The beam is supported by the wall as shown (gravity neglected). Two forces act at the centroid of the free end, Fy=10 000 N and Fz=1 000 N. Height of the web is h=0.03 m. The span of the beam is 0.5 m. a) Calculate maximum (absolute) normal stress and maximum (absolute) shear stress in the beam (consider entire beam) (15 points) b) For points A and B: Calculate principal normal stress (max, min) and principal shear stress (max). Calculate angles where these stresses appear. Note: It is enough to consider stresses in the xy-plane only. (10 points) c) Check the values and angles in part b) by drawing Mohr's circle for points A and B (10 points) d) Determine the yield stress of the ductile material used for the beam at points A and B, if safety factor is 2, according to maximum-shear-stress theory (5 points) In the small box below, write the maximum normal stress in the beam (first part of question (a)) in MPa. Solve on paper, write your name on each page, scan and upload to the next question below (within allowed time). Make sure it can be read (points will be reduced otherwise).
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The bending moment M = Fy * L = 10000 N * 0.5 m = 5000 Nm. The section modulus for a rectangular cross section is S = bh^2/6 = 0.03 m * (0.03 m)^2 / 6 = 4.5 * 10^-5 m^3. The maximum normal stress is Ļ_max = M/S = 5000 Nm / 4.5 * 10^-5 m^3 = 111.11 MPa. The maximum Show moreā¦
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Problem 2: The cantilever beam pictured is rigidly supported (fixed) at its left end and is subject to forces F and F applied to its right end. Perform a finite element analysis of this beam subject to the following guidelines. Diameter = 0.1 m Length = 0.5 m Material: AISI 1045 Steel cold drawn External Load: Assign an axial force F = 840 N that acts normal to the right end of the beam in the direction shown. Also, apply an upward force F = 740 N that acts on the top-right edge of the beam. Assign a fixed restraint to the left end (left-end face) of the beam. Determine the following: a) Use the Probe feature to create a graph of Ļx across the front face of the beam (from top to bottom) at approximately X = 0.04 m to the right of the fixed end. Use classical stress equations to calculate the appropriate normal stress on both the top and bottom surfaces of the beam and compare the percent difference. b) Calculate the maximum shear stress due to bending using classical equations at the fixed end and compute the percent difference between classical and finite element solutions for maximum shear stress determined halfway between the top and bottom surfaces of the beam.
Madhur L.
Supreeta N.
The beam shown below is supported over a length of 100 m and subjected to a 5 kN point load (at an angle of 35Ā°) that is located 25 m from the left support. Additionally, the beam is subjected to a 25 kNĀ·m moment in the center and a distributed load over a total length of 30 m (toward the right end); the exact load profile can be seen in the figure below. 100 m 25 m 25 m 20 m 15 m 15 m 20 kN/m 10 kN/m 5 kN 35Ā° 25 kNĀ·m a) Calculate the magnitude and position of the resultant force of the distributed load only. b) Determine magnitude and direction of the reaction forces in both the left and the right support. c) If the roller support on the right is swapped with the pin support on the left, does the system remain statically determinate or become statically indeterminate? Why? d) Determine the shear force and bending moment at a distance of 60 m from the left support. e) Determine the shear force and bending moment at a distance of 85 m from the left support. f) Draw the shear force diagram of the entire beam.
Adi S.
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