Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 4, Problem 4.8P
To determine
The total change of length possible for the beams in the design.
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Mechanics of Deformable Bodies Problem:
The figure shows the upper half of a built up girder( the cross section is symmetric about the neutral axis). All rivets used in fabrication have a diameter of 22 mm. The moment of inertia of the entire cross sectional area of the girder about the neutral axis is l=4770x10⁶mm⁴. The working stresses are 100 MPa for rivets in shear and 280 MPa for bearing of the web plate. If the maximum shear force carried by the girder is 450 kN, determine the largest allowable spacing of rivets that join the angles to the web plate.
A 1.0 meter long A36 steel rod with a diameter of 40mm is lightly attached at both end of the rod, end A and end B. A collar is located in the center of the rod. The initial temp is 60 degrees C. The final temperature is 35 degrees C. Determine the force that must be applied to the collar so that the reaction at B is zero.Given:Delta T=25 degrees CE for A36 steel: 200 GPaCoeff of thermal expansion: 12(10^-6)/degree C
A circular steel rod AB (diameter d1=15 mm, length
L1=1100 mm) has a bronze sleeve (outer diameter d2
21 mm, length L2=800 mm) shrunk onto it so that the two
parts are securely bonded (see figure).
Calculate the total elongation δ (mm) of the steel bar due
to a temperature rise ΔT=200oC. (Material properties are
as follows: for steel, Es=210 GPa and αs=12x10-6/C;
for bronze, Eb=110 GPa and αb=20x10-6/C.)
Chapter 4 Solutions
Materials Science And Engineering Properties
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- (a) Figure Q2 shows a steel bar held between two rigid supports. The bar has a cross sectional area of 0.25 m? and is 6.0 m in length. The structure is stress free before a force P = 3×106 N is applied at the point shown. Steel has a Young's modulus E = 210 GPa and its coefficient of thermal expansion is equal to a = 12 ×10-6 K-1. (i) What is the stress in the bar to the left of the applied load? (ii) What change in temperature would cause the stress on the right of the applied load to go to zero? 4.0 m 2.0 m P Figure Q2 -Constrained metal bar.arrow_forwardMechanics of Deformable Bodies The rigid bar of negligible weight is pinned at O and attached to two vertical rods. Assuming that the rods were initially stress-free, what is the largest load P that can be applied without exceeding stresses of 150 MPa in the steel rod and 70 MPa in the bronze rod? 21 -1.5 →1.5 Bronze Steel A = 900 mm2 E= 200 GPa L= 1.5 m A = 300 mm? E = 83 GPa L=2 marrow_forwardA steel rod having a cross-sectional area of 0.002 sq. m. and length of 1.5 m. is attached to unyielding supports. If the temperature falls 60 degrees Celsius, the modulus of elasticity of steel is 200 x 109 N/m2, and the coefficient of linear expansion is 11.5 x 10–6 per degree Celsius, finda. the deformation due to the temperature drop in mm, andb. the force exerted by the rods on the supports in kN..arrow_forward
- the resultant of two forces in a plane is 400N at 120 degrees. if one of the forces is 200N at 20 degrees what is the other forcearrow_forwardA rigid bar of negligible weight is supported as shown in the figure. If W = 80 kN, compute the temperature increase that will cause the Bronze L = 3 m A = 1300 mm E= 83 GPa 4. Steel L= 1.5 m A = 320 mm +1m-E= 200 GPa stress in the bronze rod to be 40 MPa. Assume the coefficients of linear expansion are 11.7 µm/(m-°C) for steel and 18.9 µm/(m-°C) for bronze. AT = Answers: 2.5 m 1.5 m 2/2arrow_forwardA rigid bar, AB, is pinned at point B. Two other bars, AC and AD, are connected to point A to provide support for AB. We are investigating the behavior of this system under a specific load. Key Details: Bar properties: Material: Steel with Young's modulus (Esteel) of 200 GPa and coefficient of thermal expansion (a) of 11.7 x 10^-6 /°C. Cross-sectional area: AC: 1960 mm² AD: 1250 mm² Length: AC: √2 meters (square root of 2 meters) AD: 1 meter Inclination angles: AC: θ₁ (theta 1) = 30° from horizontal AD: θ₂ (theta 2) = 20° from horizontal Load on bar AB: Idealized linearly increasing load with a maximum value of 30 kN/m at point B. Problem Objectives: Determine the internal forces (axial forces) acting within bars AC and AD due to the applied load on AB. Calculate the displacement of point A in both horizontal (dA,x) and vertical (dA,y) directions.If the bar is cooled by 10°C, what would be the: Determine the internal forces (axial forces) acting within bars AC and AD…arrow_forward
- 2. A rigid bar of negligible weight is supported as shown. If W = 80 kN, compute the temperature change that will cause the stress in the steel rod to be 55 MPa. Assume the coefficients of linear expansion are 11.7 µm/(m. °C) for steel and 18.9 um/ (m.°C) for bronze. DIN Steel L = 1.5 m A = 320 mm² 1m E= 200 GPa 2.5 m Bronze L = 3m A = 1300 mm² E = 83 GPa W 1.5 marrow_forwardA rigid bar of negligible weight is supported as shown in the figure. If W = 80 kN, compute the temperature change that will cause the stress in the steel rod to be 55 MPa. Assume the coefficients of linear expansion are 11.7 µm/(m °C) for steel and 18.9 μm/(m °C) for bronze. Steel L=1.5 m A = 320 mm² 1 mE= 200 GPa 2.5 m Bronze L-3m A-1300 mm² E=83 GPa W 1 1.5 marrow_forwardHelp me pleasearrow_forward
- A rigid bar is carried by deformable steel and aluminum rods as shown in the figure. If P = 95 kN, a = 4 m, and b = 9 m, determine the ratio of the axial deformation of aluminum to steel. (no unit)arrow_forwardThe polyvinyl chloride bar is subjected to an axial force of 900 lb. If it has the original dimensions shown, determine the value of Poisson’s ratio if the angle u decreases by Δu = 0.01° after the load is applied. Epvc = 800(103) psi.arrow_forward175 mm A 50 mm C -225 mm -300 mm Bar ACB shown in the Figure is subjected to a uniform temperature increase of 35°C. Knowing that the diameters of AC is 50 mm and CD is 75 mm, the modulus of elasticity E is 6.0 GPa, and the thermal expansion coefficient is 100x10^(-6) ?1/°C. What is the displacement of point Carrow_forward
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