The deflection of a cantilevered beam supporting the weight of an advertising sign is given byy = −Wx26EI(3L − x),where we have the following.y = deflection at a given x location (m)W = weight of the sign (N)E = modulus of elasticity (N/m2)I = second moment of area (m4)x = distance from the support as shown (m)L = length of the beam (m)A vertical brick wall extends upwards from the ground. Near the top of the wall, a cantilever of length L extends rightwards along a horizontal x-axis that begins at the wall. A sign hangs down from the right end of the cantilever.Plot the deflection of a beam with a length of 3 m, the modulus of elasticity of E = 200 GPa, and I = 1.2 ✕ 106 mm4 for a sign weighing 1,500 N. (Submit a file with a maximum size of 1 MB.)

A cantilever beam shown in the figure below is commonly used to support a load acting on a balcony.The left side of a horizontal beam is connected to a vertical wall. Eight equally spaced vertical arrows start above the beam and point downward, toward the beam. The collection of arrows is labeled w. The leftmost arrow is near the left end of the beam at the wall, and the rightmost arrow is at the right end of the beam. A point near the left end of the beam is a distance x to the right of the wall, and the length of the beam is L > x.The deflection of the centerline of the beam is given by the following equationy = −wx224EI(x2 − 4Lx + 6L2),where we have the following.y = deflection at a given location (m)w = distributed loadE = modulus of elasticity (N/m2)I = second moment of area (m4)x = distance from the support as shown (m)L = length of the beam (m)What is the appropriate unit for w if the preceding equation is to be homogeneous in units? Show all steps of your work.Starting with the equation y = −wx224EI(x2 − 4Lx + 6L2), the units of y are m, the units of the product E I are , and the units of x2, Lx, and L2, are all equal to . Rearranging the equation above to solve for w, we obtain the following. (Use any variable or symbol stated above as necessary.)w = Then, the units of w are N · m3 = .

A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2 kN normal to the top surface as shown in the figure. The Young’s modulus of elasticity of the material of the beam is 210 GPa,fl magnitude of slope (in radian) at Q (20 mm from the fixed end) is_____ :

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in N. ?2) of the beam is::

Calculate the maximum deflection of the following beam in millimetres (mm). Assume the beam is made of steel with E = 200 000 MPaPlease write your answer to 2 decimal places, do not include units in your answer and consider a downwards deflection to be positive.The formula for the deflection at the mid-span of a simply supported beam is δ = 5wL4/384EI where a positive deflection here indicates a downwards deflection.

the deflection of a beam under a load is directly proportional to the load applied.