10-116 Determine the products of inertia Iry, Iyas and Ix for the homogeneous steel (p = 7870 kg/m) block shown in Fig. P10-116. 100 mm 200 mm 200 mm 300 mm. Fig. P10-116
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Q: STRess in members BD, cD and CE
A: ##STRESS IN MEMBER BD , CD , and CE##
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Given :-
A block is shown with dimensions
Density of the homogeneous steel =
To determine :-
The products of Inertia IXY , IYZ , IZX
Mass of segment (1) will be
Similarly,
Mass of segment (2) will be
Step by step
Solved in 4 steps with 1 images
- Aluminum Bronze Steel 2P 3P P 4P - - 1.0 m 0.8 m FIG. P2.16 2.16 A compound bar consisting of bronze, aluminum, and steel segments is loaded axially as shown in the figure. Determine the maximum allowable value of P if the change in length of the bar is limited to 2 mm and the working stresses pre- scribed in the table are not to be exceeded. A (mm²) E (GPa) G, (MPa) Вronze 450 83 120 Aluminum 600 70 80 Steel 300 200 140TWO SOLID CYLINDRICAL RODS ARE JOINED AT B AND LOADED AS SHOWN. ROD AB IS MADE OF STEEL (E = 210 GPa) AND ROD BC OF BRASS (E = 108 GPa). DETERMINE (A) THE TOTAL DEFORMATION OF THE COMPOSITE ROD ABC, (B) THE DEFLECTION OF POINT B. 40 KN 400 mm 600 mm A B C 30 mm 50 KN 50 mmTwo solid cylindrical rods are joined at B and loaded as shown. Rod AB is made of steel E 200GPa and rod BC of brass E 105GPa. Determine (a) the total deformation of the composite rod ABC, (b) the deflection of point B. 250 mm 300 mm 30 kN -30 mm 40 kN -50 mm
- 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…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.At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 12.7 x 10-6/°F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 8.6 x 10-6/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and C are rigid. Determine the lowest temperature at which the two bars contact each other. (1) 3 in. 32 in. 90.2°F O 69.9°F 139.2°F 103.5°F O 111.0°F B ↑ 2 in. ↓ 44 in. -0.04-in. gap
- 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 %3DA 5.2-m-long aluminum tube (1) is to be connected to a 2.2-m-long bronze pipe (2) at B. When put in place, however, a gap of 9 mm exists between the two members, as shown. Aluminum tube (1) has an elastic modulus of 69 GPa and a cross-sectional area of 1980 mm2. Bronze pipe (2) has an elastic modulus of 93 GPa and a cross-sectional area of 3970 mm2. If bolts are inserted in the flanges and tightened so that the gap at B is closed, determine: (a) the normal stresses ?1, ?2 produced in each of the members. (b) the displacement (change in length of material (2), up is positive) uB of flange B with respect to support A. 5.2 m 2.2 m Answers: (a) 0₁ = (b) Ug = C (1) B (2) -95.40 1.126 9 mm MPa, 0₂ = mm. -47.58 MPaAt a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 14.4 x 10-6/°F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 9.6 × 10-6/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and Care rigid. Determine the lowest temperature at which the two bars contact each other. (1) 3 in. 32 in. 105.3°F 75.3°F O 147.3°F 86.6°F 113.4°F B ↑ 2 in. ↓ (2) 44 in. 0.04-in. gap
- At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 13.4 x 10-6/°F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 10.1 x 10-6/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and Care rigid. Determine the lowest temperature at which the two bars contact each other. (1) ↑ 3 in. 32 in. O 75.9°F O 146.5°F O 105.8°F O 122.3°F O 111.3°F 2 in. (2) 44 in. -0.04-in. gapA hollow aluminum tube is rigidly attached between steel rod and a bronze rod as shown. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in aluminum of 80 MPa, in steel of 150 MPa or bronze of 100 MPa. Steel Aluminum Bronze А P> ЗР - 2P outside = 30 mm d inside = 20 mm d d = 16 mm d = 60 mm -100mm- -150mm- -125mm-An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in Fig. P-108. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminum of 90 MPa, or in bronze of 100 MPa. Figure P-108 PARTNER Aluminum A=400 mm² Steel A = 500 mm² 2.5 m 2.0 m Bronze A = 200 mm² 1.5 m 2P