8. A solid aluminum cantilever beam is 40 cm in length and has a circular cross section with a diameter of 3.0 cm. Calculate the torsional stiffness of the beam, kr, in N-m/rad and the angular displacement at the end in deg when it is subjected to a moment of 20 N-m. 40 20 Cross-section 3.0
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- A simply supported beam is shown. The maximum bending moment is at B. Use the method of sections to determine the moment at B. Then determine the required section modulus needed for an allowable bending stress of 24 ksi. Verify that two L4x3 angles placed as shown will support the loading based on the angle thickness you select using Appendic C. Ans: Ms = 4350 Ib-ft %3D 2000 Ib 300 lb/ft 6 in, CTI 4 in. 3 ft 3 ftA beam has a bending moment of 2.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3 cm and internal diameter 2.3 cm. The modulus of elasticity for the material is 210 x 109 N/m. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.7 cm from the neutral axis Solution: (i) The moment of inertia = 26024.12mm^4 ii) The radius of curvature is 2186.02mm (iii) The maximum bending stress is 1.44GPA iv) The bending stress at the point 0.7 cm from the neutral axis isCalculate the beam deflection at point C. E = 206.8 GPa, I„ = 1.873 x 10-6 mª. Use either the double integration method or the moment area method. Show your work. 200 N 500 N 50.8 mm -------z 76.2 mm A 1 m 1 m 2 m
- A manufacturer wants to design a hydraulic floor crane that can lift an engine with a maximum weight of 5300 N. Two choices are considered for the beam ABC, a T‐beam and a C‐beam, as shown below. The beam has a uniform weight distribution (Ps 8000 kg/m3) Question: Calculate the area moment of inertia for each cross‐section.( for the T and C beam) note: you might have to do the parallel axis theorem to solve. And the 70mm on the top of the C beam is supposed to got to the end of the top part of the C beam and not stop at the y prime axis(the whole to of the C beam is 100mm)A beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is in (N/mm^2) Answer and unit for part 3 iv) The bending stress at the point 0.6 cm from the neutral axis is in(N/mm^2) Answer and unit for part 4Derive the formula for the bending stress of a beam with a rectangular cross section and triangular cross secrion. Thank you
- A beam has a bending moment of 4.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.8 cm and internal diameter 2.1 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis (i) The moment of inertia = ii) The radius of curvature is : (iii) The maximum bending stress is: iv) The bending stress at the point 0.6 cm from the neutral axis is :The Cantilever beam in Fig. 5, has a circular cross section (diameter-100 mm) (a)find the shear stress in the beam in points (a,b.c.d and e) due to applied the uniform load 3 kN/m and the torque 4kN.m. (2) Sketch the shear stress distribution over the cross section. Dia 100 mm B. 3 kN/m 4 kN.m C. 4 m 1 m FigA beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.7 cm and internal diameter 2.2 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.6 cm from the neutral axis is Answer and unit for part 4
- Consider an 8-m long simply supported T-beam with overhangs loaded as shown below. 200 mm w kN/m 50 mm 50 kN-m 50 kN-m 200 mm 2 m 4 m 2 m 50 mm 1. Determine the location of the neutral axis measured from the top of the beam and the moment of inertia (in mm4) of the section about its neutral axis. Draw the shear and bending moment diagrams. Annotate all relevant values and distances. Determine the magnitude of the maximum negative 2. moment. Determine the minimum allowable strength of the beam in tension and the minimum allowable strength of the beam in compression. 3. Determine the maximum allowable load, w (in kN/m), that can be applied pn the beam. 4. B.A beam with a solid homogeneous rectangular section is simply supported at A and B. A concentrated load F= 150 kilonewtons (kN) acts at point C where distance L1 (A to C) = 2.50 metres (m) and distance L2 (C to B) = 1.65 metres (m). The dimensions of the rectangular section of the beam are breadth, b = 35 mm and depth d= 125 mm. %3D Calculate the maximum bending stress and give your answer in N/mm2 to two decimal places. *Assume the weight of the beam is negligible and zero.A simply supported beam of length 4 m, is subjected to an Uniformly distributed load of 22 kN/m for entire span. It has a hollow rectangular cross section of outer width 45 mm and outer depth of 90 mm with the wall thickness of 3mm. Find (i) The maximum bending moment, (ii)Bending stress induced, (iii) Radius of curvature, (iv) Flexural rigidity. Take E as 150 GPa. The maximum bending moment (in Nm) = Maximum Bending stress induced (in MPa) = Radius of curvature (in m) =. Flexural Rigidity of the beam (in Nm2) =