S  k y y  0 (5.247) s sn sm s1 where ks is the constant for the sth spring and y represents the spring distortion. When there are many degrees of freedom, this procedure for analyzing free vibration becomes very lengthy. In such cases, it may be preferable to solve Eqs. (5.244) by numerical, trial-and-error procedures, such as the Stodola-Vianello method. In that method, the solution converges first on the highest or lowest mode. Then, the other modes are determined by the same procedure after elimination of one of the equations by use of Eq. (5.246). The procedure requires assumption of a characteristic shape, a set of amplitudes Ar1. These are substituted in one of Eqs. (5.244) to obtain a first approximation of 2. With this value and with AN1  1, the remaining N  1 equations are solved to obtain a new set of Ar1. Then, the procedure is repeated until assumed and final characteristic amplitudes agree. Because even this procedure is very lengthy for many degrees of freedom, the Rayleigh approximate method may be used to compute the fundamental mode. The frequency obtained by this method, however, may be a little on the high side. The Rayleigh method also starts with an assumed set of characteristic amplitudes Ar1 and depends for its success on the small error in natural frequency produced by a relatively large error in the shape assumption. Next, relative inertia forces acting at each mass are computed: Fr  WrAr1 /AN1, where AN1 is the assumed displacement at one of the masses. These forces are applied to the system as a static load and displacements Br1 due to them calculated. Then, the natural frequency can be obtained from

To cover a contractor for liability arising from the use by employees of their own automobiles while on the contractors business, nonownership or contingent liability coverage is necessary. This may be included in the policy by endorsement. Frequently, contractors have occasion to hire trucks or other vehicles. Liability and property damage insurance to cover the contractors liability when using hired vehicles should be included at the time automobile insurance is arranged. 17.15.4 Boiler and Machinery Insurance Boilers and other pressure vessels and machinery require the protection provided by boiler and machinery insurance. These policies cover loss resulting from accidents to boilers or machinery, and in addition, cover contractors liability for damage to the property of others. Policies may also include liability arising from bodily injuries sustained by persons other than employees. This is needed because of the exposure that many contractors have as a result of the interest of the public in

Accordingly, a means of egress is a continuous, unobstructed path for evacuees from any point in a building to a public way. Its three parts are: Exit accessthat portion that leads to an entrance to an exit Exitthe portion that is separated from all other building spaces by construction or equipment required to provide a protected path to the exit discharge Exit dischargethe portion that connects the termination of an exit to a public way Means of egress may be provided by exterior and interior doors and enclosed horizontal and vertical passageways, including stairs and escalators. (Elevators and exterior fire escapes are not generally recognized as reliable means of egress in a fire.) Exit access includes the space from which evacuation starts and passageways and doors that must be traversed to reach an exit. Types of Exits. Building codes generally recognize the following as acceptable exits when they meet the codes safety requirements: Corridorsenclosed horizontal or slightly inclined public passageways, which lead from interior spaces toward an exit discharge. Minimum floor-to-ceiling height permitted is generally 80 in. Minimum width depends on type of occupancy and passageway (Table 3.7 and Art. 3.5.11). Codes may require subdivision of corridors into lengths not exceeding 300 ft for educational buildings and 150 ft for institutional buildings. Subdivision should be accomplished with noncombustible partitions incorporating smokestop doors. In addition, codes may require the corridor enclosures to have a fire rating of 1 or 2 hr. Exit passagewayshorizontal extensions of vertical passageways. Minimum floor-to-ceiling height is the same as for corridors. Width should be at least that of the vertical passageways. Codes may require passageway enclosures to have a 2-hr fire rating. A street-floor lobby may serve as an exit passageway if it is sufficiently wide to accommodate the probable number of evacuees from all contributing spaces at the lobby level. Exit doorsdoors providing access to streets or to stairs or exit passageways. Those at stairs or passageways should have a fire rating of at least 3/4 hr. Horizontal exitpassageway to a refuge area. The exit may be a fire door through a wall with a 2-hr fire rating, a balcony providing a path around a fire barrier, or a bridge or tunnel between two buildings. Doors in fire barriers with 3- or 4-hr fire ratings should have a 11/2-hr rated door on each face of the fire division. Walls permitted to have a lower fire rating may incorporate a single door with a rating of at least 11/2 hr. Balconies, bridges, and tunnels should be at least as wide as the doors providing access to them, and enclosures or sides of these passageways should have a fire rating of 2 hr or more. Exterior-wall openings, below or within 30 ft of an open bridge or balcony, should have at least 3/4-hr fire protection. Interior stairsstairs that are inside a building and that serve as an exit. Except in one-story or two-story low-hazard buildings, such stairs should be built of noncombustible materials. Stairway enclosures generally should have a 2-hr fire rating. Building codes, however, may exempt low dwellings from this requirement. Exterior stairsstairs that are open to the outdoors and that serve as an exit to ground level. Height of such stairs is often limited to 75 ft or six stories. The stairs should be protected by a fire-resistant roof and should be built of noncombustible materials. Wall openings within 10 ft of the stairs should have 3/4-hr fire