The deflection of a cantilevered beam where supporting the weight of an advertising sign is given by 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 (mª) -Wx? (3L – x) 6EI y = x = distance from the support as shown (m) L = length of the beam (m) Plot the deflection of a beam with a length of 3 m, the modulus of elasticity of E = 200 GPa, and I = 1.2 x 10° mm4 and for a sign weighing 1500 N. What is the slope of the deflection of the beam at the wall (x – 0) and at the end of the beam where it supports the sign (x = L). L Sign Problem 18.5

1. The figure below shows a roof canopy beam which is supported by a φ20 mm hanger rod. The roof beam is a W200×19 steel beam with a cross-sectional area A = 2480 mm2, section modulus, Sx = 163×103 mm3 and a moment of inertia Ix = 16.6×106 mm4. The modulus of elasticity for steel is 200 000 MPa.  1)     Determine the beam reactions at A and B.      2)     Determine the axial stress in the 20 mm hanger rod and in the W200x19 beam.     3)     Determine the shear force and bending moment   at the midspan of the beam     4)     Determine the bending stress in the beam at the mid-span of the beam.

Hand written please

1. The following equation describes the relationship between the maximum deflection of the end of a beam and the applied load. PL3 = 3EI a) If ð is the maximum deflection in inches, L is the length of the beam in inches, P is the load in pounds, and E is the Young's Modulus in pounds/in?, find the units for I (moment of inertia). b) The measured deflection for a specific beam under loading is measured to be .01 in. Convert this to millimeters.