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- A cantilever beam has a length L = 12 ft and a rectangular cross section (b = 16 in., h = 24 in.), A linearly varying distributed load with peak intensity q0acts on the beam, (a) Find peak intensity q0if the deflection at joint B is known to be 0.18 in. Assume that modulus E = 30,000 ksi. (b) Find the location and magnitude of the maximum rotation of the beam.what are the boundary condition and continuity condition if we want to find its maximum deflection?A 70kg human steps at the tip of a springboard used to dive in a pool. The springboard has a length of 1.75 meters, moment of inertia is 0.000002 m^4, and modulus of elasticity is 150 GPa. Determine the deflection of the springboard in millimeters. Note: δ=[(W)(L^3)]/[(3)(E)(I)] for a cantilever beam with end force.
- Beam ABC is loaded by a uniform load q andpoint load P at joint C. Using the method of superposition,calculate the deflection at joint C. Assumethat L = 4 m, a = 2 m, q = 15 kN/m, P = 7.5 kN,E = 200 GPa, and I = 70.8 X106 mm4.A steel beam ABC carries a concentrated load of P (kN) at B and C, as shown in Figure Q3(a). The beam has a wide-flange section shown in Figure Q3(b) and designated as W610 x 82 with geometrical properties as shown in Table 1. Assuming that the beam behaves as elastic-perfectly plastic material with a yield strength of 210 MPa; (a) Draw the moment diagram of the beam and indicate the section that carries the maximum bending moment. (b) Knowing the shape factor of the beam, k = 1.15 calculate the magnitude of Pp (kN) for the condition of plastic collapse/hinge. (c) Determine the yielded length, Li, (m) along the beam where the section has experienced yielding corresponding to the plastic collapse condition (part (b)).A I-meter-long, simply supported copper beam (E= 117 GPa) carries uniformly distributed load q. The maximum deflection is measured as 1.5 mm. a. Calculate the magnitude of the distributed load q if the beam has a rectangular cross section (width b= 20 mm, height h= 40 mm). b. If instead the beam has circular cross section and q= 500 N/m, calculate the radius r of the cross section. Neglect the weight of the beam.
- A Rayleigh’s method approximation for the first flexural natural frequency of a beam that is simply supported at both ends was using the guessed shape lx^2-x^3. How many of the boundary conditions are satisfied with this guess?a machine mass m = 500 kg is mounted on a simply supported steel beam of length l = 2 that has a rectangular cross section (thickness = 0.1 m and width 1.2 m) and whose young modulus is given by E = 2.06x10 ^ 11 N / m2. To reduce the vertical deflection of the beam, a spring of stiffness k is added in the middle of the span, as shown in the following figure. Determine the value of k necessary to reduce the deflection of the beam by: a) -25% of its original valueb) -50% of its original valuec) -75% of its original valueMechanics of solid A simply supported beam ABCD is subjected to a uniform distributed load along AB and CD as shown in Figure Q2. The properties of the beam are: E = 70 GPa and INA = 30x10^6 mm4. (a) Determine the deflection of the beam at point B. (b)Next, change the pin support at point A to a fixed support. Develop the slope and deflection functions.
- A cantilever beam (with a clamp at x=0 and free at x=L, where L is the length of the beam) is modelled using two flexural elements. A moment, M, is applied at the free end. Which of the following describes the vector of external forces? Note that no other external forces are applied, and the degrees of freedom are defined in the usual order. f = [0 0 0 0 M 0]T f = [0 0 M 0]T f = [0 0 0 0 0 M]T f = [0 0 0 M]T f = [M 0 0 0]T f = [0 M 0 0]TConsider 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, 8.0 m, 1150 kgbeam is hinged to a wall and supportedby a thin cable attached 2.0m from the free end of the beam(Fig. ). The beam is supportedat an angle of 30.0° above thehorizontal. (a) Draw a free-body diagramof the beam. (b) Find the tensionin the cable. (c) How hard doesthe beam push inward on the wall?