Mohrs circle an also be plotted when the principal stresses are not known but the stresses x, y , and vxy , on any two perpendicular planes, are. The procedure is to plot the two points representing these known stresses with respect to the and v axies (points C and D in Fig. 5.10). The line joining these points is a diameter of Mohrs circle. Constructing the circle on this diameter, we find the principal stresses at the intersection with the axis (points A and B in Fig. 5.10). For more details on the relationship of stresses and strains at a point, see Timoshenko and Goodier, Theory of Elasticity, McGraw-Hill Publishing Company, New York. Forces that cause a member to twist about a longitudinal axis are called torsional loads. Simple torsion is produced only by a couple, or moment, in a plane perpendicular to the axis. If a couple lies in a nonperpendicular plane, it can be resolved into a torsional moment, in a plane perpendicular to the axis, and bending moments, in planes

Load, Btu per hr % of load Cfm Cellar 14,500 10.05 200 First-floor store 47,600 33.00 660 Vestibule 5,650 3.91 80 Office 4,900 3.39 70 Mens room 2,800 1.94 40 Ladies room 1,590 1.10 25 Second-floor office No. 1 33,300 23.01 460 Office No. 2 16,650 11.51 230 Mens room 2,820 1.95 40 Ladies room 2,080 1.44 30 Hall 12,585 8.70 175 q 160,000 If we adjust the flame (oil or gas) so that the output was the capacity theoretically required, the temperature rise would be q 144,475 In actual practice, we do not tamper with the flame adjustment in order to maintain the manufacturers design balance. Instead, the amount of air supplied to each room is in proportion to its load. (See Table 13.12 which is a continuation of Table 13.11 in the design of a forced-air heating system.) Duct sizes can then FIGURE 13.5 One-pipe hot-water heating system. be determined for the flow indicated in the table (see Fig. 13.5). In this example, minimum duct size for practical purposes is 12  3 in. Other duct sizes were obtained from Table 13.7, for a friction loss per 100 ft of 0.15, and equivalent rectangular sizes were obtained from Table 13.6 and shown in

Programmable thermostats conserve energy by automatically raising or lowering the space temperature to preprogrammed settings several times each day. Building temperature adjustment is performed during occupied or unoccupied hours, again conserving energy. Other types of thermostats are available that produce energy savings: Reduction of overshoot on recovery from the setback temperature, limiting the rate of temperature rise Selective recovery from the setback temperature by utilizing lower stages (singlestage and multistage only) Selective recovery from the setback temperature using a heat pump in lieu of an auxiliary heat source (heat-pump thermostat) Prevention of room temperature from deviating from a setpoint under varying load conditions Microprocessor-Based Systems. Computerized energy-management systems are available to control complex HVAC systems. These microprocessor-based systems are capable of saving enough energy that they can pay for themselves in 2 years or less. Energy management systems are available in many variations and with many features. The most common include the following capabilities: equipment scheduling, duty cycling of equipment, temperature compensated control, demand limiting, optimum start / stop, and night setback. Equipment Scheduling. Running HVAC equipment on a continuous basis, including periods when operation is not required, results in excessive and nonproductive energy consumption. These periods include lunch hours, evenings, weekends, and holidays. By using a scheduling program, the control panel promptly shuts down HVAC units and other units at preset times. A typical scheduling program may provide four start / stop times for each load on an 8-day cycle. It will also allow automatically for holidays, leap year, and daylight savings time. Duty Cycling. Duty cycling applied to HVAC equipment utilizes an on-off control to reduce operating time and increase energy savings. The duty-cycling program will permit up to eight cycle patterns for each load. On-off protection timers are provided for each piece of equipment to assure equipment safety. Temperature-Compensated Control. Maximum occupant comfort is ensured by use of a computerized control that provides equipment cycling with automatic temperature override. Cycling will be reduced or stopped, depending on whether room temperatures fall outside present comfort levels. Hence, the guesswork of selecting proper cycling strategies is eliminated. Demand Limiting. As much as 50% of bills for use of electrical energy may be attributed to kW demand charges. A demand-limiting program may save a substantial amount of utility energy costs over a short period of time. A computerized control, in particular, can limit costly demand charges by use of a predictive demand program that anticipates electrical demand peaks. When the control panel senses that a peak is about to occur, it simply turns off selected loads on a priority basis until the peak subsides, thereby reducing the energy bill. Optimum Start /Stop. Energy can be wasted by HVAC equipment that is scheduled to start and stop on worst-case conditions. This scheduling results in operations that begin too soon and run too long. Computerized control monitors indoor and outside temperatures and determines the most efficient start and stop times without sacrificing individual comfort. Optimum start / stop also allows independent control of individual comfort zones. Night Setback. Utilization of night setback temperatures saves energy by automatically converting the specific comfort zone to a predetermined nighttimetemperature setpoint. The setpoint overrides the daytime setting for every load or zone. HVAC equipment will operate to maintain the nighttime setting until morning warm-up or cool-down is required. Night setback also allows independent control