The following data exists, E=71GPA, I=5x10*m , h=1m, l2=2m, mi=m2=1500kg, l=4m, mw 200kg mE.I m; т, 1, Figure 3 Modelling an aircraft wing. Determine the equivalent mass of the system referred to the wing tip (i.e. if we replaced the system with an equivalent system consisting of a massless cantilevered beam with single lumped mass placed at the free end, what would be the value of meg?). 7777
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- A shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shatt carries four masses (150 + 01) kg, (200 + 01) kg, (250 +01) kg and (300 + 01) kg. These masses are located at a distance of 1.5m, 2.5 m, 5.5 mand 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m? and mass density for the shaft material is 7500 kg/m?3. Determine critical speed of the shaft in revolutions per minute for the following two cases: 1. Effect of the mass of the shaft is neglected. 2. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?A safety valve (pressure relieve valve) on top of a pressure vessel containing steam under pressure p = 2 MPa, has a discharge hole of diameter d = 10 mm as shown in the figure below. The valve is designed to release the steam when the pressure reaches the maximum allowable value pmax = 2.23 MPa. If the free height (i.e., uncompressed height) of the spring hfree = 135 mm and its spring stiffness k = 5 kN/m, what should be the dimension h of the valve?A fixed beam AB, 5 m long, is carrying a point load at its centre. The moment of inertia of the beam is 60 x 106 mm4 and modulus of elasticity for beam material is 2.2 x 105 N/mm2. End moments are taken to be 40 kN-m. The load at the centre is
- Question 1) In the beam whose loading condition is given in the figure, F force F= 79 kN, w1 distributed load w1= 44 kN/m, w2 distributed load w2= 55 kN/m, θ angle θ= 49° and L length L= 9 m given. According to this;Question 1-A) Find the support response in the y direction (By) at point B. (Enter your result without writing kN units.)Question 1-B) Find the support response in the y direction (Ay) at point A. (Enter your result without writing kN units.)Question 1-C) Find the support response in the x direction (Ax) at point A. (Enter your result without writing kN units.)A beam supported by three identical springs at points A,B,C (see figure). Given that flexural of rigidity of the beam, EI= 2.029X1011 N.mm2 ; spring constant = 1471.5N/mm, w=116N/mm All dimensions are in mm. 1. What are the reaction force RA,RB,RC?Consider a wooden rectangular slab of mass M, length L, and width W nailed vertically to a wall. The nail is located approximately at the middle of the top edge (see Figure 1). You use a hammer to hit the bottom right corner with an average force F, and the hammer is contact with the slab for a small time Δt. The moment of inertia for the axis passing through the center of the slab, pointing away from the wall, is I=(1/12)M(L^2+W^2). a) What is the angular speed of the slab about the nail just after you have hit the slab? Explain every part of your working carefully; in particular, state any assumptions you make. Hint: consider ττ=dL/dt. Use the torque due to the force exerted by the hammer. b) What is the angular speed of the slab when the slab becomes vertical (see Figure 2)? You should be able to do this even if you didn't manage to do the previous part. What is the minimum value of F for a given Δt such that the slab does become vertical? c) What would have happened if the nail was…
- A uniform beam, of mass 31 kg/m run, is simply supported on a span of3.6 m. Taking EI for the beam as 7 MN.m2, calculate the frequency oftransverse vibrations.This frequency is to be reduced by 40% by fixing three equal masses tothe beam, at the mid-point and the quarter points. Calculate how muchthese masses should be.(Q1) A uniform beam, of mass 31 kg/m run, is simply supported on a span of3.6 m. Taking EI for the beam as 7 MN.m2, calculate the frequency oftransverse vibrations.This frequency is to be reduced by 40% by fixing three equal masses tothe beam, at the mid-point and the quarter points. Calculate how muchthese masses should be. (Q2) A beam 6 m long, simply supported at each end, carries a load of 6 t/mrun, extending from a point 1.2 m from one support to another point 4.2m from the same support. EI for the beam is 110 MN.m2. The mass of thebeam itself may be neglected.Determine the frequency of transverse vibrations of the beam in avertical plane:a) very roughly, assuming the whole load to be concentrated at itscentre of gravity.b) more accurately, by treating the load as three equal concentratedloads applied at suitable points. (Dunkerley's method issuggested.)In the given fig shows the suspension system of a freight truck with a parallel-spring arrangement. Find the equivalent spring constant of the suspension if each of the three helical springs is made of steel with a shear modulus G = 120GPaand has five effective turns, mean coil diameter D = 50 cm, and wire diameter d = 5 cm
- A machine of mass 2000kg originally placed at midspan of a simply supported beam of length 1.2 m having a rectangular cross -section (depth = 0.1 and width +1.2 m) and young's modulus of elasticity 206 GPa. To reduce the vertical deflection of the beam, two springs with the same stiffness will be attached at midspan, see figure below. A.) Determine the value of the stiffness of the spring to reduce the deflection of the beam by 10%, B.) What is the natural frequency of the system?A spade is modelled as a uniform rod, of mass 2kg and length 90cm, attached to a uniform square lamina, of side 20cm and mass 0.5kg. A gardener holds the spade horizontally with hands 30cm and 60cm from the end of the rod. Find the vertical forces exerted by the gardener's hands. Im stuck on this question. Pls help meA beam segment subjected to internal bending moments at sections A and B is shown along with a sketch of the cross-sectional dimensions. The beam segment is subjected to internal bending moments of MA = 1390 N·m and MB = 3080 N·m. The segment length is Δx = 180 mm. Consider area (2) and use cross-sectional dimensions of b = 92 mm, d = 240 mm, and d2 = 68 mm. (a) sketch a side view of the beam segment and plot the distribution of bending stresses acting at sections A and B. Indicate the magnitudes of key bending stresses on the sketch, including the stresses at the top and bottom of area (2) on both sections A and B. Tensile stresses are positive, while compressive stresses are negative. (b) determine the resultant forces acting in the x direction on the specified area at sections A and B, and show these resultant forces on the sketch. Tensile forces are positive, while compressive forces are negative. (c) determine the magnitude of the horizontal force required to satisfy equilibrium…