Draft

8.3Reactions 159

ROOF

q = 1.4 k/ft

FRAME

+ q = 0.2 k/ft

ROOF

q = 1.4 k/ft

FRAME

q = 1.6 k/ftTOTAL

+ q = 0.2 k/ft

Figure8.3:MagazziniGenerali;Loads(BillingtonandMark1983)

8.3 MagazziniGenerali;Loads(BillingtonandMark1983).

5 Reactionsforthebeamaredetermined rsttakingadvantageof symmetry, Fig. 8.4:

W = (1:6)k/ft(63:6)ft= 102k (8.2-a)

R =

W

2

=

102

2

= 51 k (8.2-b)

We notethatthesereactionsareprovidedby theinternalshearforces.

63.6 ft

51 k 51 k

TOTAL

q = 1.6 k/ft

Figure8.4:MagazziniGenerali;BeamReactions,(BillingtonandMark1983)

8.4 MagazziniGenerali;BeamReactions,(BillingtonandMark1983).

6 Theinternalforcesarepimarilytheshearandmoments.Thosecanbe easilydeterminedfor

a simplysupporteduniformlyloadedbeam. Theshearvarieslinearlyfrom 51 kipto -51kip

withzeroat thecenter,andthemoment diagramis parabolicwiththemaximummoment at

thecenter,Fig.8.5, equalto:

Mmax=

qL

2

8

=

(1:6)k/ft(63:6)ft

2

8

= 808 k.ft (8.3)

7 Theexternallyinducedmoment at midspanmustbe resistedby an equalandoppositeinternal

moment. Thiscanbe achieved througha combinationof compressive forceontheupper bers,

andtensileonesonthelower.Thus thenetaxialforceis zero,however thereis a netinternal

couple,Fig.8.6.