Assume the temperature is always uniform throughout the rail and they arefree to expand on the rail ties without friction or other impediments.40 ftInches-RRad-8"CENTRE UNE OF BOLT HOLESRad-8"laches-P. R. R. STANDARD RAIL SECTION.100 LBS, PER YARD.Inches= The 40 ft. long steel rails on the train track are placed such that there issmallgap,8, between them to allow for thermal expansion. A 100 Ib/yardarail has a cross-sectional area of 9.80 in?. The steel used has the followingmaterial properties:E = 29,000 ksi6.6 HE/ F(a) What is the size of gap, 8, required so that the rails just touch oneanother when the temperature increases from -20°F to 100°F.(b) Given the gap you found in (a), what would the axial force in the railsbe if the temperature rises to 130°F.

Axial tension force is the force acting on rails in its axial direction. It's a pulling force that…

Answered: The 40 ft. long steel rails on the…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A 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…
3) An bronze rod is rigidly attached between a aluminum rod and a steel rod as shown. Axial loads are applied at the positions indicated. Find the maximum allowable value of P that will not exceed a stress in steel of 140MPA, in aluminum of 90MPA or in bronze of 100MPа. Aluminum A = 500mm? Bronze A = 200mm? Steel A = 150mm2 2P ЗР L st = 1.2m L br = 2m Lal = 3.5m
2. A rod is composed of an aluminum section rigidly attached between steel and bronze sections as shown in the figure. Axial loads are applied at the positions indicated. The cross-sectional area of the rod is 300sq.mm. Express your answer in MPa. Determine the stress in the steel. b. a. Determine the stress in the aluminum. Determine the stress in the bronze. C. STEEL ALUMINUM BRONZE 56kN 14kN -0.6m- -0.9m- -0.76m-
k=17 p=117kN Strength of material question. without taking into account wire thickness.
A 260 mm bar AB with a rectangular cross section of 17 x 30 mm, consists of two aluminium layers with cach being 6 mm thick and brazed to a centre steel layer of 5 mm thickness as shown in Figure Q3. An axial tensile force of P- 37 kN is applied to the assembly by means of a rigid end cap at B. Given that the assembly is fixed at end A and the Young's modulus of aluminium and steel are E.= 70 GPa, Es= 200 GPa, respectively, determine: i Whether this structural configuration is statically determinate or statically indeterminate, and clearly explain your reasoning. ii. The normal forces in the aluminium layers and the steel layer i. The normal stress in the aluminium layers and the steel layer. State whether the stresses are in tension or compression iv. Determine the deformation of the assembly Cross section of the bar 6 mm 5 mm 6 mm 30 mm 260 mun Aluminium. Steel- Aluminitum Nא 37 30 mm
3. A steel bolt through a 31-in long aluminum tube has the nut turned on until it just touches the end of the tube. No stress is introduced on the bolt or the tube. The temperature of the assembly is raised from 70 to 81 degrees Fahrenheit. The cross-sectional area of the bolt is 0.09 sq. inch and the cross-sectional area of the tube of 0.30 sq. inch. a. Find the thermal deformation (in inches) of the steel bolt. (Write your answer to 6-decimal places.) b. Find the thermal deformation (in inches) of the aluminum tube. (Write your answer to 6-decimal places.) c. Find the stress (in psi) induced in the steel bolt by the temperature change. d. Find the stress (in psi) induced in the aluminum tube by the temperature change.
Steel 1 m Aluminum T 0.75 m Determine the maximum permissible value of T subject to the following conditions: tt S 80 MPa, Tal 50 MPa, and the angle of rotation of the free end is limited to 0.1 radian. For T. Hollow Solid d= 30 mm D= 40 mm %3D steel, G = 82 GPa and for aluminum, G= 28 GPa. %3D d = 30 mm %3D
etermine the elongation of a 0.5-in, dianeter sterl bar The elastic modulus of the steel bar is 27000 kar. 2000 Ib 10 ft
Q/ Find the Maximum stresses in Steel and Aluminum. Est= 210G pa and E al%3D 70 G pa ? W= 15 Kn.M 120mm 5m Al steel 60mm 140 mm
Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area of 1.71 in and an elastic modulus of 2050 ksi. Bar (2) has a cross-sectional area of 1.019 in? and an elastic modulus of 3910 ksi. Assume L-20 in. Lyn47 in. Q-6 kips. P-3.6 kips, and R-13.2 kips. Determine the horizontal deflection of end Crelative to end A. (1) (2) Answer: UCIA - in.
A mild steel flat of width 120 mm and thickness 10 mm is bent into an arc of a circle of radius 10 m by applying a pure moment 'M'. If E is 200 GPa, then magnitude of the pure moment 'M' will be
3. A steel bolt through a 25-in long aluminum tube has the nut turned on until it just touches the end of the tube. No stress is introduced on the bolt or the tube. The temperature of the assembly is raised from 70 to 79 degrees Fahrenheit. The cross-sectional area of the bolt is 0.08 sq. inch and the cross-sectional area of the tube of 0.25 sq. inch. For steel: E = 30 x 10^6 psi, coefficient of thermal expansion = 6.5 x 10^-6 per degree Fahrenheit. For aluminum: E = 10 x 10^6 psi, coefficient of thermal expansion = 13.0 x 10^-6 per degree Fahrenheit. Find the thermal deformation (in inches) of the steel bolt. (Write your answer to 6-decimal places. ) * Your answer This is a required question Find the thermal deformation (in inches) of the aluminum tube. (Write your answer to 6-decimal places.) * Your answer This is a required question Find the stress (in psi) induced in the steel bolt by the temperature change. * Your answer

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