HOW LOAD DISTRIBUTED FROM SLAB TO BEAM AS PER YIELD LINE THEORY(AS PER IS 456) ~ civilimp

HOW LOAD DISTRIBUTED FROM SLAB TO BEAM AS PER YIELD LINE THEORY(AS PER IS 456)

in this blog, I will tell you how load can be distributed on beam from the slab. please see the whole blog for a better understanding

The Yield analysis was proposed by Ingerslev in 1923

SLAB IN ETABS :

the slab is modeled as a floor object in ETABS.in ETBAS slabs can be modeled as shell or membrane.

if we model slab as membrane then we can assign property like one way or two way in our slab .but if we model slab as a shell we cant give property like one way or two way

for load distribution from slab to beam Emembrane follow yield line theory

TYPES OF SLAB :

1)according to the architect: ribbed, waffle, and flat slab

RIBBED SLAB

WAFFLE SLAB

2)according to support :

simply supported, cantilever, continuous, etc

3)according to the method of construction :

precast, prestressed, cast in situ

4)according to load distribution:

one way, two way

4a) ONE WAY :

1) if ly /lx≥2 then the slab is one way

FIG :1

in figure 1 AB, CD, AC and BD are the beams. let's assume in figure 1 ly/lx >2 then the slab load is only distributed on a longer beam AB and CD and the value of the load on beam AB and CD will be the same

distributed load on beam AB and CD is given by W kn/m

in one way slab, there is no load distribution on a shorter span that why on beam AC and BD there is no load

now the value of the load 'W' is

RECTANGULAR LOAD VALUE ( rectangular)= P×l_x/2 ( l_xin meter)

where P is the total slab load

P=1.5 ⟦{slab thickness(in meter) × density of concrete(in KN/M³)}+Liveload+ floor finish⟧

P=1.5 ⟦ {(d×25)+L.L+F.F}⟧

where d =slab thickness,

L.L =live load

F.F= floor finish

now W=P(in KN/M^2) ×l_x/2 (l_xin meter)

l_x_{=shorter span of the beam}

W= load on beam in KN /m

2 ) if ly /lx=2 then the slab is one way but the load distribution on the beam is different.

triangular load distribution on beam AB,CD,BD,AC

all load values on the beam are the same

TRIANGULAR LOAD VALUE 'W'=P×l_x/3

where P is the total slab load

P=1.5 ⟦{slab thickness(in meter) × density of concrete(in KN/M3)}+Liveload+ floor finish⟧

P=1.5 ⟦ {(d×25)+L.L+F.F}⟧

where d =slab thickness,

L.L =live load

F.F= floor finish

now W=P(in KN/M^2 ) ×l_x/3 (l_xin meter)

l_x=shorter span of the beam

4b) TWO WAY :

if l_y/l_x <2 then the slab is two way

in a two-way slab, the load is distributed on the beam as trapezoidal load and triangular load

triangular load ( W_Triangle ) OAC and KBD are the same

TRIANGULAR LOAD

1st) VALUE OF TRIANGULAR LOAD ( W_Triangular )=P×l_x/3

where P is the total slab load

P=1.5 ⟦{slab thickness(in meter) × density of concrete(in KN/M³)}+Liveload+ floor finish⟧

P=1.5 ⟦ {(d×25)+L.L+F.F}⟧

where d =slab thickness,

L.L =live load

F.F= floor finish

now W_Triangular=P(in KN/M^2 ) ×l_x/3 (l_xin meter)

l_x=shorter span of the beam

and trapezoidal load ( W_Trapezoidal ) OKAB and OKCD are the same

trapezoidal load

1st) VALUE OF TRAPEZOIDAL LOAD ( W_Trapezoidal ) =P×l_x/3⟦1-1/3k²⟧

where k = l_y/l_x

where P is the total slab load

P=1.5 ⟦{slab thickness(in meter) × density of concrete(in KN/M3)}+Liveload+ floor finish⟧

P=1.5 ⟦ {(d×25)+L.L+F.F}⟧

where d =slab thickness,

L.L =live load

F.F= floor finish

now

( WTrapezoidal ) =P×lx/3⟦1-1/3k2⟧

l_x=shorter span of the beam

these load distributed on a slab

HOW LOAD DISTRIBUTED FROM SLAB TO BEAM AS PER YIELD LINE THEORY(AS PER IS 456)