7. In class, we derived material indices for stiffness-limited designs. In stiffness-limited designs, it is elastic...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
7. In class, we derived material indices for stiffness-limited designs. In stiffness-limited designs, it is elastic deflection that is the active constraint. However, in strength-limited design, deflection is acceptable given that the component does not fail, so strength here is the active constraint. Derive the material index for selecting materials for a beam of length (L), specified strength, and minimum weight. Assume that the beam has a solid square cross section (t x t). Equations for the failure load of a beam and the second moment of the cross-section are given below. Here, ym is the distance between the neutral axis of the beam and its outer filament. 10000 1000 Strength, of (MPa) 100 10 (a) List the design requirements, e.g., function, constraints, objective, and free variables. (b) Derive the material index for this strength-limited design for minimum mass. 0.1 8. Suppose that the beam in Q7 must support a design load of 750 kN and it has dimensions of 1 m in length and 0.25 m in width and height. By looking at the strength vs. density chart given below, which material or materials would be your choice? 0.01- Strength Density Metals and polymers: yield strength Ceramics and glasses: MOR Elastomers: tensile tear strength Composites: tensile failure 0.01 Foams Rigid polymer foams Natural materials 0.1 Polymers and elastomers Free Composites. Cork Wood, PMMA Flexible polymer foams CFRP Mg alloys, GFRP PEEK Butyl rubber Ceramics SigN4 Ti alloys Steels SIC AlO3 Al alloys Silicone elastomers Ff 1 = Density, p (Mg/m) Zinc alloys Concrete = 12 Iof YmL 10 A 12 Ni alloys/ Metals Tungsten alloys Lead alloys Tungsten carbide Copper alloys Guidelines for minimum mass design 7. In class, we derived material indices for stiffness-limited designs. In stiffness-limited designs, it is elastic deflection that is the active constraint. However, in strength-limited design, deflection is acceptable given that the component does not fail, so strength here is the active constraint. Derive the material index for selecting materials for a beam of length (L), specified strength, and minimum weight. Assume that the beam has a solid square cross section (t x t). Equations for the failure load of a beam and the second moment of the cross-section are given below. Here, ym is the distance between the neutral axis of the beam and its outer filament. 10000 1000 Strength, of (MPa) 100 10 (a) List the design requirements, e.g., function, constraints, objective, and free variables. (b) Derive the material index for this strength-limited design for minimum mass. 0.1 8. Suppose that the beam in Q7 must support a design load of 750 kN and it has dimensions of 1 m in length and 0.25 m in width and height. By looking at the strength vs. density chart given below, which material or materials would be your choice? 0.01- Strength Density Metals and polymers: yield strength Ceramics and glasses: MOR Elastomers: tensile tear strength Composites: tensile failure 0.01 Foams Rigid polymer foams Natural materials 0.1 Polymers and elastomers Free Composites. Cork Wood, PMMA Flexible polymer foams CFRP Mg alloys, GFRP PEEK Butyl rubber Ceramics SigN4 Ti alloys Steels SIC AlO3 Al alloys Silicone elastomers Ff 1 = Density, p (Mg/m) Zinc alloys Concrete = 12 Iof YmL 10 A 12 Ni alloys/ Metals Tungsten alloys Lead alloys Tungsten carbide Copper alloys Guidelines for minimum mass design
Expert Answer:
Answer rating: 100% (QA)
The question provided relates to material selection for a strengthlimited design of a beam with the goal of minimizing mass The image attached shows a StrengthDensity plot with different materials and ... View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
Students also viewed these mechanical engineering questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
A nutritionally defective E. coli strain grows only on a medium containing thymine, whereas another nutritionally defective strain grows only on a medium containing leucine. When these two strains...
-
For the machine element shown, locate the x coordinate of the center of gravity. r 40 mm 60 mm 50 mmo 10 mm 10 mm 50 mm r-30 mm 60 mm 10 mm
-
Sellers Construction Company purchased a compressor for $28,000 cash. It had an estimated useful life of four years and a $4,000 salvage value . At the beginning of the third year of use, the company...
-
What does Section 404 of the Sarbanes-Oxley Act of 2002 require? (a) A 10-year jail sentence and $1 million fine for violations of the act. (b) Rotation of audit partners every five years. (c) A...
-
During the third calendar quarter of 20--, the Beechtree Inn, owned by Dawn Smedley, employed the persons listed below. Also given are the employees' salaries or wages and the amount of tips reported...
-
Task Rank order the vendors, keeping Amazon's goals in mind. Rank 1 K 2 B Shipped On Time Cost to Amazon Vendor Customer Issues Quantity Shipped E 3 R 4 F O Low Amount Moderate Amount < B High Amount...
-
You want to purchase a home based upon your current salary you decide that you can afford $2000.00 per month. Your bank has approved you for a (30 year) loan at an interest rate of 5%. 1) Based upon...
-
Answer the following Situation: Mr. B, a trying hard socialite, went to Boracay for some rest and relaxation. Upon reaching the island, he immediately went to Station 1 where Starbucks was located....
-
If -y - y = 2x then find at the point (1, 2) in simplest form. da
-
Find (2 2 + /2 - 5 - 6 ) dz x4 x C x
-
If log (3x-2)=4, then what is the value of x? B
-
For y = In x+1 Find dx =?
-
If f(x) = +2, find f'(x) =
-
Find the general solution of the homogeneous linear equation a)y" + 7y = 0 b)y" 6y' + 25y = 0
-
XYZ Inc. a calendar year, accrual basis corporation, had the following items during 2021: Gross revenue from operations Cost of goods sold $420,000 ($180,000) $9,000 LT capital gain .LT capital...
-
Policy Application: Distortionary Taxes in General Equilibrium: Consider, as in exercise 16.10, a 2-person exchange economy in which I own 200 units of x1 and 100 units of x2 while you own 100 units...
-
Trade, Migration and the Price of a Haircut: In the text, we discussed the similarities between outsourcing and immigration and with it the similarity between trading goods and moving workers. The...
-
Return to the case of our beer and pizza consumption from end-of-chapter exercise 6.3. A. Again suppose you consume only beer and pizza (sold at prices p1 and p2 respectively) with an exogenously set...
-
Cruz Manufacturing Ltds sales slumped badly in 2019. For the first time in its history, it operated at a loss. The companys income statement showed the following results from selling 600 000 units of...
-
The following are emails from various students to Dr. Destiny Sands, who is a professor in the English Department. These students are wondering if Dr. Sands would let them register for her...
-
What are some flawed assumptions about workplace communication? What is the reality for each myth?
Study smarter with the SolutionInn App