I have the answers for part a just need help with b mostly thanks P1=3mMin.Ms.t.$-0.0001/≤0σ-σ≤020t-R≤00.02 R ≤0.20.001 HW2-2:Design a hollowed circular beam shown in the figure with minimum mass and satisfy thefollowing conditions:1) When P = 50 kN, the axial stress σ should be no more than σ where σ= P/A and σ = 250 MPa,2) When P = 0, the deflection of the beam & due to beam weight should satisfy ♪≤0.00017, where / is thelength of the beam and 8= 5w/4/384EI. Note that w is the weight per unit length (unit: N/m), mass densityis p=7800 kg/m³, modulus of elasticity is E = 210 GPa, second moment of area is I=лR³t, andgravitational constant is g = 9.80 m/s².3) The ratio of R to t must satisfy R/t> 20; and4) The design limits are t = [0.10, 1.0] cm and R = [2.0 to 20.0] cm.2R1=3ma. Write the standard formulation of this optimization problem.b. Solve this problem using GimOPT with 1, 10, and 100 initial points and report your solutions (Do notattached input files in your solutions. You may use an excerpt from your output file to show the results).Note: Pay attention to units and make sure your units in your standard formulation are consistent.

import numpy as npfrom scipy.optimize import minimize# Constants (SI units)rho = 7800 # kg/m^3l = 3…

P 1=3m Min. M s.t. $-0.0001/≤0 σ-σ≤0 20t-R≤0 0.02 R ≤0.2 0.001 20; and 4) The design limits are t = [0.10, 1.0] cm and R = [2.0 to 20.0] cm. 2R 1=3m a. Write the standard formulation of this optimization problem. b. Solve this problem using GimOPT with 1, 10, and 100 initial points and report your solutions (Do not attached input files in your solutions. You may use an excerpt from your output file to show the results). Note: Pay attention to units and make sure your units in your standard formulation are consistent.

P 1=3m Min. M s.t. $-0.0001/≤0 σ-σ≤0 20t-R≤0 0.02 R ≤0.2 0.001 20; and 4) The design limits are t = [0.10, 1.0] cm and R = [2.0 to 20.0] cm. 2R 1=3m a. Write the standard formulation of this optimization problem. b. Solve this problem using GimOPT with 1, 10, and 100 initial points and report your solutions (Do not attached input files in your solutions. You may use an excerpt from your output file to show the results). Note: Pay attention to units and make sure your units in your standard formulation are consistent.

Principles of Foundation Engineering (MindTap Course List)

8th Edition

ISBN:9781305081550

Author:Braja M. Das

Publisher:Braja M. Das

Chapter6: Vertical Stress Increase In Soil

Section: Chapter Questions

Problem 6.4P: Refer to Figure P6.4. A strip load of q = 900 lb/ft2 is applied over a width B = 36 ft. Determine...

See similar textbooks

Similar questions

Refer to Figure P6.4. A strip load of q = 900 lb/ft2 is applied over a width B = 36 ft. Determine the increase in vertical stress at point A located z = 15 ft below the surface. Given: x = 27 ft. Figure P6.4
Two line loads q1 and q2 of infinite lengths are acting on top of an elastic medium, as shown in Figure P8.6. Find the vertical stress increase at A.
The data in Table 1.5.3 were obtained from a tensile test of a metal specimen with a rectangular cross section of 0.2011in.2 in area and a gage length (the length over which the elongation is measured) of 2.000 inches. The specimen was not loaded to failure. a. Generate a table of stress and strain values. b. Plot these values and draw a best-fit line to obtain a stress-strain curve. c. Determine the modulus of elasticity from the slope of the linear portion of the curve. d. Estimate the value of the proportional limit. e. Use the 0.2 offset method to determine the yield stress.
A tensile test was performed on a metal specimen having a circular cross section with a diameter 0. 510 inch. For each increment of load applied, the strain was directly determined by means of a strain gage attached to the specimen. The results are, shown in Table: 1.5.1. a. Prepare a table of stress and strain. b. Plot these data to obtain a stress-strain curve. Do not connect the data points; draw a best-fit straight line through them. c. Determine the modulus of elasticity as the slope of the best-fit line.
The results of a tensile test are shown in Table 1.5.2. The test was performed on a metal specimen with a circular cross section. The diameter was 3 8 inch and the gage length (The length over which the elongation is measured) was 2 inches. a. Use the data in Table 1.5.2 to produce a table of stress and strain values. b. Plot the stress-strain data and draw a best-fit curve. c. Compute the, modulus of elasticity from the initial slope of the curve. d. Estimate the yield stress.
A tensile test was performed on a metal specimen with a diameter of 1 2 inch and a gage length (the length over which the elongation is measured) of 4 inches. The dam were plotted on a load-displacement graph. P vs. L. A best-fit line was drawn through the points, and the slope of the straight-line portion was calculated to be P/L =1392 kips/in. What is the modulus of elasticity?
EB and FG are two planes inside a soil element ABCD as shown in Figure 10.50. Stress conditions on the two planes are Plane EB: EB = 25 kN/m2; EB = +10 kN/m2 Plane FG: FG = 10 kN/m2; FG = 5 kN/m2 (Note: Mohrs circle sign conventions for stresses are used above) Given ; = 25, determine: a. The maximum and minimum principal stresses b. The angle between the planes EB and FG c. The external stresses on planes AB and BC that would cause the above internal stresses on planes EB and FG
A structural member with a rectangular cross section as shown in the accompanying figure is used to support a load of 2500 N. What type of material do you recommend be used to carry the load safely? Base your calculations on the yield strength and a factor of safety of 2.0.
How does a tensile stress differ from a compressive stress?
A 10 cm long rectangular bar (when subjected to a tensile load) deforms by 0.1 mm. Calculate the normal strain.
In concrete work, Fuller and Thompson (1907) suggested that a dense packing of grains can be achieved if the percent finer (p) and grain size (D) are related by the following equation, where n is a constant varying in the range of 0.3-0.6. Dmax is the size of the largest grain within the soil. p=(DDmax)n100 This equation is sometimes used in roadwork for selecting the aggregates. a. For n = 0.5, show that the soil is well graded. b. If n = 0.5 and Dmax = 19.0 mm, find the percentages of gravel, sand, and fines within the soil. Use the Unified Soil Classification System.
For the beam shown: (a) determine the distance a for which the maximum positive and negative bending moments in the beam are equal; and (b) draw the corresponding shear and bending moment diagrams for the beam.