In the case of two-way slab systems, which are statically indeterminate, detailed inelastic analysis (yield line analysis) is conducted. The moment coefficients given in the Code IS 4!"#$$(Table #!) for two-way rectangular slabs with various %ossible edge conditions are based on &ield 'ine nalysis. &ield line analysis* is the e+uivalent for a two-dimensional fleural member (%la (% late te or
slab sl ab))
of th the e li limi mitt
anal an alys ysis is of
a
one ne-d -dim ime ens nsio iona nall
memb me mbe er
(continuous beam), &ield lines Ty%ical crac %atterns generated when ultimate moment is reached Characteristics of yield lines are, i) &ield lines are straight ii) &ield lines end at su%%orting edges of slab iii) &ield lines %asses through intersection of ais of rotation of ad/acent slab elements iv) is of rotation lies along lines of su%%orts and %asses over columns
Fig: Typical interior panel in a two-way slab system
Fig: Yield line pattern under uniformly distributed collapse load
Fig: Deected shape at collapse (section A-A)
Assumptions of Yield ine Theory: The following are the assumptions of the yield line analysis of reinforced concrete slabs:
0. The steel reinforcement is fully yielded along the yield lines at colla%se. 1otation following yield is at constant moment. #. The slab deforms %lastically at colla%se and is se%arated into segments by the yield lines. The individual segments of the slab behave elastically. 2. The elastic deformations are neglected and %lastic deformations are only considered. The entire deformations, therefore, tae %lace onlyalong the yield lines. The individual segments of the slab remain %lane even in the colla%se condition. 4. The bending and twisting moments are uniformly distributed along the yield lines. The maimum values of the moments de%end on the ca%acities of the section based on the amount of reinforcement %rovided in the section. . The yield lines are straight lines as they are the lines of intersection between two %lanes.
!ules of yield lines: The two terms, %ositive and negative yield lines, are used in the analysis to designate the yield lines for %ositive bending moments having tension at the bottom and negative bending moments having tension at the to% of the slab, res%ectively. The following are the guidelines for %redicting the yield lines and aes of rotation" 0. &ield lines between two intersecting %lanes are straight lines. #. 3ositive yield line will be at the mid-s%an of one-way sim%ly su%%orted slabs. 2. egative yield lines will occur at the su%%orts in addition to the %ositive yield lines at the mid-s%an of one-way continuous slabs.
4. &ield lines will occur under %oint loads and they will be radiating outward from the %oint of a%%lication of the %oint loads. . &ield line between two slab segments should %ass through the %oint of intersection of the aes of rotation of the ad/acent slab segments. !. &ield lines should end at the boundary of the slab or at another yield line. 5. &ield lines re%resent the aes of rotation. 6. Su%%orted edges of the slab will also act as aes of rotation. 7owever, the fied su%%orts %rovide constant resistance to rotation having negative yield lines at the su%%orted edges. 8n the other hand, aes of rotation at the sim%ly su%%orted edges will not %rovide any resistance to rotation of the segment. 9. is of rotation will %ass over any column su%%ort, if %rovided, whose orientation will de%end on other considerations
