6. 將分別為 4 及 8 歐姆（Ω）電阻串連，接上 12 伏特(V)電源， 其 4 歐姆（Ω）電阻兩端之電壓為_____伏特(V)。

Problem 1 (25%)A cylindrical pressure vessel with flat ends is subjected to a torque T and tensile forces P. The tank has a radius r = 125 mm and the wall thickness t = 6.5 mm. The loads are T = 850 N·m, P = 400 kN, and the internal pressure p = 7.25 MPa.Determine the maximum shear stress τmax in the wall of the cylinder.

Problem 2 (25%)Draw the shear-force and bending-moment diagrams for the beams shown in the figure below.

Problem 3 (25%)Using moment-area method, obtain formula for the maximum deflection δmax at the midpoint for a simple beam AB with a uniform load of intensity q.

Problem 4 (25%)A stepped shaft ACB is held against rotation at ends A and B and subjected to a torque T0 acting at section C. The two segments of the shaft have diameters dA and dB, respectively, and polar moments of inertia IpA and IpB, respectively. The shaft has length L and segment AC has length a. For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft?

1. A W200×59 steel column shown in Fig. 1-1 and Table 1-1 is made of material with modulus of elasticity E of 200 GPa and yielding stress σy of 250 MPa. The column is fixed at its base and braced at the top so that it is fixed from displacement, yet free to rotate about the y-y axis; also, it can sway to the side in the y-z plane. Determine the maximum eccentric load (P) the column can support before either the column begins to buckle or the steel of the column yields.(25%)Secant Formula:

1) Plot the moment diagram and shear diagram of the beam.

2) Compute the rotational angle of the beam at point B.

3) Identify the value and location of the maximum curvature in the beam.

1) Find the absolute maximum shear stress at the location of the strain gages in terms of p, r and t.

2) If εb=3εc, find the value of Poisson's ratio v for the material of the vessel.

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