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8 Analysis of Rigid The effect of the rotation shown in Fig. 3 is that the resultant of the soil reactions becomes eccentric. If the resultant, V, is removed a dis tance, a, from the theoretical midpoint, the product of V X a is the moment that counteracts the rotation and restrains the footing. Under the con ditions given in Fig. 3, the soil offers little restraint against rotation of the footing. Analyses show that the restraining moment VXa is a small fraction of the moment, M in Fig. 2 (b), that is required for fixity, and that the stresses in the frame are but slightly affected by the moment, VXa. It is therefore reasonable to assume the hinged condition in Fig. 2 (a) for the ordinary rigid frame bridge, provided the footings are comparatively narrow. If the degree of restraint is expected to be particularly large, it is advis able to make allowance for the restraint by assuming the maximum distance of a that may prevail under conditions similar to those in Fig. 3. The frame should be analyzed accord ingly as though it had imaginary hinges a dis tance, a, from the theoretical midpoint. It is not deemed necessary to consider restraint at the footings of the rigid frame analyzed in Problems 1 to 9, since the footings are only 6 feet wide and are supported on a soil with an allowable carrying capacity of 5,000 p.s.f.* SECTION IV—MOMENT OF INERTIA The relative values of moment of inertia, /, affect the distribution of moments and shears in continuous frames. The approximate dimensions must therefore be known before the frame can be analyzed. Moments of inertia for design of rigid framesf with rectangular cross- sections may be taken as ♦p.s.f.: pounds per square foot; p.s i.: pounds per square inch. tSee Bibliography, reference No. 31. Generated on 2015-11-26 09:26 GMT / http://hdl.handle.net/2027/coo.31924003881277 Public Domain, Google-digitized / http://www.hathitrust.org/access_use#pd-google

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8 Analysis of Rigid

The effect of the rotation shown in Fig. 3 is that the resultant of thesoil reactions becomes eccentric. If the resultant, V, is removed a dis

tance, a, from the theoretical midpoint, the product of V X a is the momentthat counteracts the rotation and restrains the footing. Under the conditions given in Fig. 3, the soil offers little restraint against rotation of thefooting. Analyses show that the restraining moment VXa is a small

fraction of the moment, M in Fig. 2 (b), that isrequired for fixity, and that the stresses in theframe are but slightly affected by the moment,VXa.

It is therefore reasonable to assume thehinged condition in Fig. 2 (a) for the ordinaryrigid frame bridge, provided the footings arecomparatively narrow. If the degree of restraintis expected to be particularly large, it is advisable to make allowance for the restraint byassuming the maximum distance of a that mayprevail under conditions similar to those inFig. 3. The frame should be analyzed accordingly as though it had imaginary hinges a dis

tance, a, from the theoretical midpoint.It is not deemed necessary to consider restraint at the footings of the

rigid frame analyzed in Problems 1 to 9, since the footings are only6 feet wide and are supported on a soil with an allowable carrying capacityof 5,000 p.s.f.*

SECTION IV—MOMENT OF INERTIAThe relative values of moment of inertia, /, affect the distribution of

moments and shears in continuous frames. The approximate dimensionsmust therefore be known before the frame can be analyzed.

Moments of inertia for design of rigid framesf with rectangular cross-

sections may be taken as

♦p.s.f.: pounds per square foot; p.s i.: pounds per square inch.tSee Bibliography, reference No. 31.

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