1) Consider a chunk of fluid that is initially shaped as shown hanging off of the edge of a table in the earth's gravity field. Ignore any forces due to the air. Prove that the fluid cannot maintain its shape by analyzing the section labeled "A" (Hint: begin by assuming that A does maintains its shape and does not move ...) water

A solid, circular, cast-iron bar (E = 12.5 X 106 psi, ν = 0.3) of diameter 2.13 inch, and height 15 inch is compressed by axial force P = 42,000 lb as in the figure below. (a) Find the change of height (inch), and (b) find the change of diameter (inch) of the bar. Neglect the weight of the bar.

Question 3 Consider the I-shaped bridge beam cross-section shown below. Assume each beam has fy = 400 MPa. Use your spreadsheet to compute Mr (considering c = 0.65 and s = 0.85) for each of the beam configurations noted in the table below. Discuss the effect of changing fc, h, As, A's and bf,top on Mr. Discuss what is the most effective, and least effective way, to increase Mr. Assume a web thickness, bw of 150 mm. bf top 60 175 Beam F 40 900 2800 0 1300 Variable f'c (Mpa) h (mm) As (mm²) A's (mm²) bf,top (mm) Beam A 40 900 2800 0 650 h 75 Beam B 20 900 2800 0 650 475 Beam C 40 1800 2800 0 650 As 200 Beam D 40 900 5600 0 650 Beam E 40 900 2800 1400 650

Question 1 A uniform bar of length L, cross-sectional area A, and mass density p is suspended vertically from one end. (a) Show that the elongation of the bar is & = pgl?/(2E) where g is the gravitational acceleration and E is the modulus of elasticity. (b) If the mass of the bar is M, show that 6 = MgL//2EA)