A WT8 $\times 25$ structural steel section (see Appendix B for its cross-sectional properties) is used for a $20-\text{ft}$ column. Assume that pinned connections are at each end of the column. Determine (a) the slenderness ratio. (b) the Euler buckling load; use $E=29,000\ \mathrm{ksi}$ for the steel. (c) the axial stress in the column when the Euler load is applied.

If you collect a jar of water from a stream, what part of its load will settle to the bottom of the jar? What portion will remain in the water indefinitely? What part of the stream's load would probably not be represented in your sample?

The load of 2000 lb is to be supported by the two vertical steel wires for which

$$σ_γ = 70 ksi.$$

Originally wire AB is 60 in. long and wire AC is 60.04 in. long. Determine the cross-sectional area of AB if the load is to be shared equally between both wires. Wire AC has a cross-sectional area of 0.02 in². Eₛₜ = 29.0(10³) ksi.

The maximum safe load uniformly distributed over a one-foot section of a two-inch-wide wooden beam is approximated by the model Load=$168.5 d^{2}-472.1$, where d is the depth of the beam. Evaluate the model for d=4, d=6, d=8, d=10, and d=12. Use the results to create a bar graph.

Consider a Zener diode circuit. The Zener diode voltage is $V_{\mathrm{Z}}=6.8 \mathrm{~V}$ at $I_{\mathrm{Z}}=0.1 \mathrm{~mA}$ and the incremental Zener resistance is $r_z=20 \Omega$. (a) Calculate $V_O$ with no load $\left(R_L=\infty\right)$. (b) Find the change in the output voltage when a load resistance of $R_L=1 \mathrm{k} \Omega$ is connected.

A three-bar, pin-jointed, planar truss supports a single horizontal load $P$ at joint $B$. Joint $C$ is free to move horizontally. The allowable stress in tension is $\left(\sigma_T\right)_{\text {alkre }}=$ $140 \mathrm{MPa}$, and the allowable stress in compression is $\left(\sigma_C\right)_{\mathrm{allsw}}=$ $-85 \mathrm{MPa}$. If the truss is to support a maximum load $P_{\text {allow. }}=50 \mathrm{kN}$, what are the required cross-sectional areas, $A_i$, of the three truss members?

The following three parallel-connected three-phase loads are fed by a balanced three-phase source: Load 1: 250 kVA, 0.8 pf lagging, Load 2: 300 kVA, 0.95 pf leading, Load 3: 450 kVA, unity pf. If the line voltage is 13.8 kV, calculate the line current and the power factor of the source. Assume that the line impedance is zero.

The stress-strain diagram for a steel alloy having an original diameter of $0.5$in and a gage length of $2$ in. is given in the figure. Determine approximately the modulus of elasticity for the material, the load on the specimen that causes yielding, and the ultimate load the specimen will support.

The steady-state voltage drop between the load and the sending end of the line seen in Fig. P10.30 is excessive. A capacitor is placed in parallel with the $200 \mathrm{kVA}$ load and is adjusted until the steady-state voltage at the sending end of the line has the same magnitude as the voltage at the load end, that is, $6400 \mathrm{~V}$ (rms). The $200 \mathrm{kVA}$ load is operating at a power factor of $0.6$ lag. Calculate the size of the capacitor in microfarads if the circuit is operating at $60 \mathrm{~Hz}$. In selecting the capacitor, keep in mind the need to keep the power loss in the line at a reasonable level.

Three loads are connected in parallel to a $120 \angle 0^{\circ} \mathrm{V}$ rms source. Load 1 absorbs 60 kVAR at pf = 0.85 lagging, load 2 absorbs 90 kW and 50 kVAR leading, and load 3 absorbs 100 kW at pf = 1. (a) Find the equivalent impedance. (b) Calculate the power factor of the parallel combination. (c) Determine the current supplied by the source.

The total power measured in a three-phase system feeding a balanced wye-connected load is 12 kW at a power factor of 0.6 leading. If the line voltage is 208 V, calculate the line current

$$I_L$$

and and the load impedance

$$Z_Y.$$

A plant consumes 60 kW at a power factor of 0.75 lagging from a 240-V rms 60-Hz line. Determine the value of the capacitor that when placed in parallel with the load will change the load power factor to 0.9 lagging.

Draw a dc load line for the transistor circuit in Fig. 28–25, and indicate the values of $I_\text{C(sat)}$, $V_\text{C(off)}$, $I_\text{CQ}$, and $V_\text{CEQ}$ on the load line.

Consider an emitter-follower amplifier. An average power of $0.5 \mathrm{~W}$ is to be delivered to a load of $R_L=8 \Omega$. (a) What are the peak values of ac output voltage and ac load current? (b) The minimum collector current occurs when $V_O$ reaches the maximum negative value. If the minimum collector current is to be 10 percent of $I_O$, determine $I_O$. (Use the results of part (a).)