At a temperature of 11°C, a 2-mm gap exists between two polymer bars and a rigid support, as shown in the figure. Bars (1) and (2) have coefficients of thermal expansion of a₁ = 122 x 10-6/°C and a2 = 80 x 10-6/°C, respectively. The supports at A and Care rigid. Determine the lowest temperature at which the 2-mm gap is closed. Assume L₁= 580 mm and L₂ = 320 mm. Gap g (1) Answer: T = i L₁ B L2 °℃ (2) с
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- 5. In the CN Railwayproject,steel railroad rails of 9.5meters long are to be installed.If the modulus of elasticity of steel is207GPa, and if the lowest temperature considered is 18°C and a maximum temperature of 36°C is designed for, determine the clearance between the rails such that adjoining will just touch at maximum design temperature. Assume α for steel is 11.6 x 10-6/°CA bar with a solid square cross-section is composed of three sections of equal length. The outer sections are made from material A and the middle section is made from material B, as shown in the figure. Assume the stress-strain curves for the particular materials used are as shown. a. What is the change in the length of the bar if a tensile load of 112 kN is applied? The square cross-section has 2 cm sides and the length of each part is 2 m The elastic modulus of material A is 150 GPa and the elastic modulus of material B is 100 GPa. b. When the bar in Part B is unloaded, it will have a permanent change in length. What is this permanent change in the length?Determine the instantaneous stress and elongation of a 30 mm diameter bar if a mass of 60 kg falls through a height of 60 mm on to a collar which is rigidly attached to the bottom end of the bar as shown in Figure Q2. The bar is 1.2 m long and is suspended vertically. The Modulus of elasticity, E, for the material of bar is 210 GPa. Take g = 10 m/s2.
- A [0/90/0/±45]s Glass/Epoxy laminate is subjected to the following mechanical loads: Nx =Ny= 80*10^5 N/m. The thickness of each lamina is 0.25 mm. Longitudinal modulus of elasticity = E1 = 38.6 GPa , Transverse modulus of elasticity = E2 = 8.27 GPa , Poisons Ratio 0.26. a) Determine the local stresses at the top of 45° plyAn engineering machine component operating in a high temperature environment consists of a copper pipe having a cross-sectional area of 2 000 mm2 and 0.3 m long, which is placed between two rigid caps. Four M22 steel bolts are symmetrically arranged around the tube and parallel to the axis of the tube and are lightly tightened. 3.1 Find the stress in the pipe and the bolts if the temperature of the assembly is increased from 25 0C to 95 0C. 3.2 What load will each bolt carry at the raised temperature? 3.3 Make a neat sketch of the assembly. (ESt = 200 GPa, ECu = 100 GPa, αSt = 12 × 10-6/ oC, αCu = 16 × 10-6/ oC)There is a gap c = 1mm between the rods in the picture, the temperature changes evenly quantitatively ΔT = 1.9°C. Calculate the normal force on the cross section of the rods. E1 = 200 GPa, L = 1.0 m, E2 = 80 GPa, A1 = 5000 mm2, A2 = 2000 mm2, α1 = 12*10-61/°C, α2 = 8*10-61/°C
- A steel rod with varying cross-sectional areas is fixed at both ends, as shown in the figure below. L1=100mm, L2=50mm, A1=300mm2, A2=100mm2. The elastic modulus is ?=2×105???, and the material has a thermal expansion coefficient of ?=12×10-6°C-1. Assuming that the rod is stress-free at 10°C . a. Calculate the normal stress in the rod assuming temperature increases to 30°C. b. Draw the normal force diagram at 30°C, with the origin and direction of x axis indicated by the red arrow.The stress-strain curve of cellulose acetate at 25°C is shown below. Draw the curves at 0°C and 60°CA circular rod and a 0.1-in.-thick rectangular bar are both made of a plastic material that has an elastic modulus of E = 2.3 GPa and a Poisson’s ratio of ν = 0.33. The rod and the bar are initially the same length L. After a particular load is applied, the 3.6-in.-wide rectangular bar is elongated by some amount ΔL and its width is reduced by 0.096 in. If the 1.3-in. diameter rod is stretched by the same amount ΔL, determine its change in diameter. Expansion is positive, while contraction is negative.
- A high-density polyethylene [E = 128 ksi; α= 88 x 10-6/°F; υ = 0.4] bar is positioned between two rigid supports. The bar is square with cross-sectional dimensions of 2.50 in. by 2.50 in. and length L = 48 in. At room temperature, a gap of Δ=0.25 in. exists between the block and the rigid support at B. After a temperature increase of 120°F, determine: a) The normal stress in the bar b)The lonitudinal strain in the bar. c)The transverse (ie lateral) strain in the bar.The steel rails of a railroad are 12 m with a clearance of 3 mm at 15 oC. Calculate: 1.1 The change in temperature that will cause the rails to touch. 1.2 The stresses that would be induced at this new temperature if there were no initial clearance (E = 200 GPa and α = 12 × 10-6 /oC).The cylindrical AC aluminum and CB steel bars in the figure are combined and placed between two rigid plates at A and B, but there is a gap of A=0.1 mm between the B plate and the bars. The modulus of elasticity of aluminum is E-70 GPa and the cross-sectional area is A-400 mm², the modulus of elasticity of steel is Eç-210 GPa and the cross-sectional area is -200 mm³. the lengths of the bars are LAC-200 mm and L CB-600 mm. Since a load of P-30 kN is applied to point C What is the stress in the AC aluminum bar?