# Slab Design

Topics: Beam, Construction terminology, Reinforced concrete Pages: 6 (640 words) Published: January 15, 2013
Tributary Areas
Many floor systems consist of a
reinforced concrete slab supported on a rectangular grid of
beams. Such a grid of beams
reduces the span of the slab and
thus permits the designer to
reduce the slab thickness. The
distribution of floor loads on floor
beams is based on the geometric
configuration of the beams
forming the grid.
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Tributary area of columns A1,

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Girders on all four sides

Theoretical Tributary Areas
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Theoretical Tributary
Beam Areas

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Theoretical Tributary
Beam Areas

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Typical Floor Framing System

Floor Beam

Girder

Simplified Floor Beam and

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Distribution Problem
The floor system of a library
consists of a 6-in thick reinforced concrete slab resting on four floor steel beams, which in
turn are supported by two steel
girders. Cross-sectional areas
of the floor beams and girders
are 14.7 in2 and 52.3 in2,
respectively as shown on the
next page figure.
Determine the floor loads on the
floor beams, girders, and
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columns.

Floor Slab – Floor Beam –
Girder – Column Schematic

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Reduction
Recognizing that the probability
of supporting a large, fully loaded
tributary area is small; building
codes permit reductions in the
when the influence area (AI =
KLLAT) is larger than 400 ft2
(37.2 m2) as given in the
following formulas:

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L = L0 ⎜ 0.25+

KLL AT ⎠

US Units

4.57 ⎞
L = L0 ⎜ 0.25+

KLL AT ⎠

SI Units

0.50 L0 ≤ L ≤ L0
for single floor members

0.40 L0 ≤ L ≤ L0
for multi-floor members

AT ≡ tributary area ft2 (m2)

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(IBC2000 – Table 1607.9.1)
Type of Element
Interior column
Exterior column without
cantilever slabs
Edge columns with cantilever
slabs
Corner columns with
cantilever slabs
Edge beams without
cantilever slabs
Interior beams
All other beams

KLL
4
4
3
2
2
2
1
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Strength Design
The forces (e.g., axial force,
moment, and shear) produced
need to combined in a proper
manner and increased by a load
factor in order to provide a level
of safety or safety factor.
minimum strength for which
members need to be designed,
also referred to as required
factored strength. ASCE 7-98
combinations:
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(1): 1.4 D
(2): 1.2 (D + F + T) + 1.6 (L + H)
+ 0.5 (Lr or S or R)
(3): 1.2 D + 1.6 (Lr or S or R)
+ (0.5 L or 0.8 W)
(4): 1.2 D + 1.6 W + 0.5 L
+ 0.5 (Lr or S or R)
(5): 1.2 D + 1.0 E + 0.5 L
+ 0.2 S
(6): 0.9 D + 1.6 W + 1.6 H
(7): 0.9 D + 1.0 E + 1.6 H
The load multipliers are based on
combination occurring as well as
the accuracy with which the
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T = Temperature or selfstrain load
Design of a member or of a
segment of a member must be
based on the load case that
produces the largest force
/stress/displacement value. 14

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Force Envelope
Forces in a particular structural
component are caused by (1)
loads acting on the structure and
is a plot of the maximum and minimum force responses along the length of a member due to any
combination.

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