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STRUCTURES ][
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STRUCTURES ][
STEELL BEAMS DEFLECTION
CALCULATIONS
METHODS
3.Safe Load Table
Figure 9.2 P&A 282-284
Max. Load:
for the following conditions:
simple span beam
total uniformly distributed load
loaded in the plane of their minor axis (y-y)
A 36 steel
lateral bracing spaced not farther than Lc
if conditions not full-filled use calculation method
Load Table - Maximum Load
Example:
A simple span beam
of A 36 steel
is required to carry a total uniformly distributed
load of 40 kips
on a span of 30 ft.
Find the lightest shape permitted.
Find the shallowest shape permitted.
Table 9.2 P&A 283
W 21 x 44 43.5
W 18 x 46 42.0
W 16 x 50 43.2
W 14 x 53 41.5
W 21 x 44 43.5 lightest member
least amount of steel
maximized on steel
W 14 x 53 41.5 shallowest member
maximize headroom
Maximum Deflection:
1. Use Deflection Factor
from Table 9.2 P&A 282, 283, 284
Maximum deflection = deflection factor / depth of beam
beam depth = first number
(keep in mind this is them maximum
allowable deflection!
actual deflection depends on actual load)
2. Use Graph
Figure 9.2 P&A 286
works both for braced and
unbraced beams
need allowable bending moment
Load Table Deflection Calculation:
Example:
A simple span beam
of A 36 steel
is required to carry a total univormly distributed
load of 25 kips.
on a span of 24 ft
while sustaining a maximum deflection of no
more than 1/360 of the span.
Find the lightest shape permitted.
A. Given:
span 24 ft
load 25 kips
max. deflection l/360
B. Asked
lightest shape
C. Graph:
W = 25 kips
____________________
V V
L = 24 ft
D = L/360
D. Calculations:
1.
D = actual load x deflection factor
--------------------- --------------------------------
table load beam depth
D = 25 x 14.3
------------------------ ----------------------------------
25.6 16
D = 0.873 inches
2. Allowable Deflection:
24 ft x 12 = 0.80 inches
-------------------
360
3. The next heavier shape from Taple 9.2
is a W 16 x 31
4. Deflection
D = 25 x 14.3
----------------------------- ----------------------------
31.5 16
D = 0.709 inches
5. Allowavle deflection 0.80 inches
6. Actual < Allowable
7. o.k.
DESIGN OF LATERALLY UNSUPPORTED BEAMS
========================================
Fig 9.2 P&A 286
various unbraced lengths
total allowable moment
1. determine max. bending moment
2. unbraced length
3. any beam whose graph lies
above or to the right of this point
is adequate
the nearest solid-line graph
representing the shape of the least weight
For beams supported laterally at intervals
greater than Lc
but not greater than Lu
the allowable bending stress is reduced
from 24 to 22 ksi
the various table values may be reduced
by the proportion
22/24 = 0.917
Expanded Equivalent Tabular Loads
The tables for
simple span beam
total uniformly distributed load
A 36 steel
can be expanded for other load cases:
for 2 loads at the third point of the beam
Case 3 Fig 3.27 P&A 109
W x L = P x L
---------- --------------
8 3
W = 2.67 x P
Fireproofing P&A 291 Fire: steel mild steel columns beams trusses rebar high-tensile cables rod high-strength alloys and heat-treated steel loose strength more rapidly permanently weakened if heated above 300 - 400 degrees C mild steel looses strength slower regains nearly all of original strength during cooling Variation with temperature of ultimate strength for steel alloys types of steel % OF STRENGTH AT ROOM TEMPERATURE Temperature Mild Cold drawn High strength (degree C) Steel prestressing alloy bars 20 100 100 100 100 102 97 98 200 115 94 102 300 112 80 97 400 82 55 82 500 55 34 60 600 30 16 38 700 20 8 20
Fire Protection of Steel 1. Encasement heavier = part of weight for beam materials: concrete min. concrete coverage masonry masonry anchors lath & plaster chicken wire cement stucco drywall 2 hour rating 2 layers of 5/8" Fire-X sheetrock 2. Sprayed-on lighter weight fibrous coating cementitious coating special paint 3. Protection System Sprinkler System Water Cooled Structure example: US Steel Pitsburg, 1976 tubular structure Centre Pompidou Paris, 1976
©Dr. Gruenwald 1996, 1997
