Solid Waste Engineering
3rd Edition
ISBN: 9781305635203
Author: Worrell, William A.
Publisher: Cengage Learning,
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Chapter 4, Problem 4.9P
To determine
The proof that the characteristic size in the Rosin-Rammler equation is the point where
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The thin square plate shown is uniformly deformed such that €, = +1445 pE, E, = -674 uE, and y,y = +1260 urad. Determine the normal
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This is the diameter in the particle size distribution curve that corresponds to 10% finer.
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- The following data were collected from a 0.4-in.-diameter test specimen of polyvinyl chloride (l0 5 2.0 in.): Load (lb) 0 Δl (in.) 0.00000 300 600 900 1200 1500 1660 1600 0.00746 0.01496 0.02374 0.032 0.046 0.070 (maximum load) 0.094 1420 0.12 (fracture) After fracture, the total length was 2.09 in. and the diameter was 0.393 in. Plot the engineering stress strain curve and calculate (a) the 0.2% offset yield strength; (b) the tensile strength; (c) the modulus of elasticity; (d) the % elongation; (e) the % reduction in area; (f) the engineering stress at fracture; and (g) the modulus of resilience.arrow_forward3. Consider iron and its elastic constants (Find them from the net or some book). An iron specimen consists of grains with texturing distribution of [110] (20%), [112] (20%), [111] (30%) and [103] (30%) (all percentages by volume) along the loading direction is serving under a static force of 10,000 N. The metal rod has a 20 mm diameter perpendicular to the loading direction. a) Find the strain response of the specimen.arrow_forwardA rigid bar is supported by two copper ro ds and the gap (A) between the aluminu m rod and the bar is 1.50 mm. If the temp erature for all materials is increased by 4 0 degrees Celsius, will the aluminum rod touch the rigid bar or not? Prove your ans wer by stating computed data. Disregard the weight of the rigid bar. For each copper bar, A = 500 mm^2, E = 120 GPa, and a = 1 6.8 μm/(m. C). For the aluminum bar, A = 400 mm^2, E = 70 GPa, and a = 23. 1 μm/(m. C).(* Copper Aluminum Copper 750 mmarrow_forward
- A student wants to measure the strain at a particular point K on a loaded specimen, so she affixes a 45° strain rosette at point K and obtains the following results: €A = 390 μrad EB = 275 μrad Ec = 325 prad After packing up and going home to analyse her results, she realises that the strain rosette was misaligned by 0 degrees CW (where a negative corresponds to CCW) from the x-y axes-ie. Gauge C is not parallel with the x-axis and is instead parallel with a different x' axis that is rotated by 0 degrees-where: 0 = 16 deg Instead of replacing the rosette and retaking measurements, the student realises she can use what she learned in ENGG2400 to find the strains she's interested in. b 45° 45° a) Draw a diagram of the situation, showing both the x-y axes and the strain rosette. b) Calculate Exx, Eyy and Yxy. c) Calculate the maximum in-plane shear strain and the associated average normal strain. I Xarrow_forward1. A vertical pressure of 70 MPa is applied to an aluminum cube sample with a length of 10 cm on each side. The modulus of elasticity of aluminum is 70000 MPa and the Poisson ratio is 0.3. a) Find the new dimensions of the cube b) What will be the new dimensions if 70 MPa pressure is applied in the horizontal directions in addition to the 70 MPa pressure in the vertical direction?arrow_forwardA 20-mm-wide block is firmly bonded to rigid plates at its top and bottom. When the force P is applied the block deforms into the shape shown by the dashed line. (Figure 1) Part A Determine the magnitude of P. The block's material has a modulus of rigidity of G= 24 GPa .Assume that the material does not yield and use sma angle analysis. Express your answer to three significant figures and include the appropriate units. Figure µA ? Value kN P = 150 mm- You have already submitted this answer. Enter a new answer. No credit lost. Try again. 0.5 mm -- Submit Previous Answers Request Answer 150 mm Provide Feedback Next >arrow_forward
- A 5-mm-thick rectangular alloy bar is subjected to ajtensile load P by pins at A and B, as shown in the figure. The width of the bar is w = 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, =710 με and ε,--255 με (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 24 kN, what is the modulus of elasticity for this specimen? Answers: (a) v= (b) E= GPaarrow_forwardW o No. Load Elongation Lo P(KN) SL(mm) |(mm) Area O eng (KN/m²) Еeng (mm) m² 1 100 36.1 2 38 0.02 100 36.1 3 76.2 0.12 100 36.1 4 92.7 0.25 100 36.1 107 0.50 100 36.1 6. 149 2.03 100 36.1 7 160.6 3.55 100 36.1 8 102 3.87 100 36.1 9 100.7 4.01 100 36.1 10 98.33 4.12 100 36.1 11 155 4.65 100 36.1 12 142 5.1 100 36.1 13 124.2 5.84 100 36.1arrow_forwardCreep exercises You are involved in a design for high temperature alloys and have performed a rupture test of material A and B. After data analysis, you noticed that the master curve (o vs LMP) of both material A and B coincide as shown in the diagram below. Based on the rupture strength o (MPa) AtB LMP = T(C+ Int) Which material will you select if they both have same constant (CA= CB)? Which material will you select if C < C? Motivate your answer by means of a calculation.arrow_forward
- The (G-E) diagram obtained in the tensile test performed on a metal sample with a diameter of 16 mm is as follows. The loads at points A, B and C and the elongation measured on l. 16 cm gauge length were determined as follows: B A B C Load (kgf) 4800 8400 7200 Elongation (mm) 0.192 28.8 38.4 a) Calculate the proportionality limit, modulus of elasticity, tensile strength, maximum uniform elongation, and contraction-elongation ratio of the metal. b) Since the measured diameter of the metal at break is 12 mm, find the constriction ratio and the actual stress at break.arrow_forwardThe (G-E) diagram obtained in the tensile test performed on a metal sample with a diameter of 16 mm is as follows. The loads at points A, B and C and the elongation measured on l. 16 cm gauge length were determined as follows: B A B C Load (kgf) 4800 8400 7200 Elongation (mm) 0.192 28.8 38.4 c) Calculate the fracture work and the maximum elastic energy the metal rod can store. d) Find the cross-sectional area of a 6 m long rod made of this metal such that it can carry 12 tons of load with 2 times the safety of yield strength. How long does the rod extend under this load?arrow_forwardConsider a cylindrical metal 6 mm in diameter and 50 mm long ispulled in tension. It is known that yield strength and elastic (Young’s) Modulus of thematerial are 200 MPa and 100 GPa, respectively, and its Poisson’s Ratio is 0.3.(a) Determine whether the deformation is elastic or plastic when 6000 N is applied.(b) Calculate specimen elongation (∆l) and reduction in diameter (∆d) when 5000 N isapplied? What are the values ∆l and ∆d when the load is released?(c) If necking occurs at a load of 8850 N, determine the UTS of the metal.(d) Calculate the ductility in terms of % E.L. if the length of the specimen at fracturepoint is 56.0 mm.arrow_forward
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