A lossless open circuited transmission line behaves as an equivalent capacitance of Ceq = Tan (BL) Show for BL << 1 that Ceq = C'L where L is the length of the transmission line and wZo C' is the lumped parameter capacitance per unit length of the transmission line. Hint: For x small, Tan(x) = x.

4. Two links made of heat treated 6061 aluminum (Sy = 276 MPa, Sys = 160 MPa) are pinned together using a steel dowel pin (Sy = 1398 MPa, Sys = 806 MPa) as shown below. The links are to support a load P with a factor of safety of at least 2.0. Determine if the link will fail first by tearout, direct shear of the pin, bearing stress on the link, or tensile stress at section AA. (Hint: find the load P for each case and choose the case that gives the smallest load.) P 8 mm P 8 mm ¡+A 3 mm →A 10 mm P

= A generator with VG 300V and R = 50 is connected to a load R = 750 through a 50 lossless transmission line of length L = 0.15 m. (a) Compute Zin, the input impedance of the line at the generator end. (b) Compute and V. (c) Compute the time-average power Pin delivered to the line. (d) Compute VL, IL, and the time-average power delivered to the load, PL (e) How does Pin compare to PL? Explain.

A1.4- Determine the factored moment resistance for the flanged beam (simply supported) shown in Figure 4. Given: Beam span L = 8m fc = 25MPa fy=400MPa As = 3-35M *350* mm 1.5 m Figure 4 *350* mm -60mm

A2.3- a simply supported reinforced concrete beam of rectangular cross-section is shown in Figure 3. The beam supports a uniform dead load of 20 kN/m (excluding the beam self-weight) and a uniform live load of 20 kN/m. The beam width is restricted to 400 mm. The maximum aggregate size is 20 mm. We are using 10M bars for stirrups and 25M bars for tension steel. Concrete is type N with f'c = 35 MPa and fy = 400 MPa. The beam needs to have 2hr fire rating. Design the beam for the given load, considering the reinforcement ratio p < 0.5 pb Figure 3 WDL = 20 kN/m WLL= 20 kN/m 8.0 m

1. For a feature other than a sphere, circularity is where: A. The axis is a straight line B. The modifier is specified with a size dimension C. All points of the surface intersected by any plane perpendicular to an axis or spine (curved line) are equidistant from that axis or spine D. All points of the surface intersected by any plane passing through a common center are equidistant from that center 2. What type of variation is limited by a circularity toler- ance zone? A. Ovality B. Tapering C. Bending D. Warping 3. How does the Rule #1 boundary affect the application of a circularity tolerance? A. The modifier must be used. B. The feature control frame must be placed next to the size dimension. C. The circularity tolerance value must be less than the limits of size tolerance. D. Circularity cannot be applied where a Rule #1 boundary exists. 4. A circularity tolerance may use a modifier. A. Ø B. F C. M D. ℗ 5. A real-world application for a circularity tolerance is: A. Assembly (i.e.,…

3. A steel bar is pinned to a vertical support column by a 10 mm diameter hardened dowel pin, Figure 1. For P = 7500 N, find: a. the shear stress in the pin, b. the direct bearing stress on the hole in the bar, c. the minimum value of d to prevent tearout failure if the steel bar has a shear strength of 175 MPa. support column pin bar thickness of bar = 8 mm h d 150 mm

A press that delivers 115 strokes per minute, each stroke providing a force of 7826 N throughout a distance of 18 mm. The press efficiency is 90% and is driven by a 1749-rpm motor. Determine average torque that must be provided by the motor in the units of N-m.

For the regulated power supply circuit, assume regular diodes with 0.7V forward drop. Use a 15V (peak), 60Hz sine wave at the transformer secondary and assume a maximum ripple level of 1V. (a) Compute the unknown components needed to design 10V DC supply.Hint: find R first, and then C. What is the ripple level for C=22µF?Sketch the rectified, filtered, and regulated outputs