Chapter 2. Primary Loads: Dead Loads and Live Loads
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Principles of Structural Design: Wood, Steel, and Concrete
Live Loads
Live loads also act vertically down like dead loads but are distinct from the latter as they are not
an integral part of the structural element. Roof live loads, Lr, are associated with maintenance of a
roof by workers, equipment, and material. They are treated separately from the other types of live
loads, L, that are imposed by the use and occupancy of the structure. The ASCE 7-05 specifies the
minimum uniformly distributed load or the concentrated load that should be used as a live load for
the intended purpose. Both, the roof live load and the floor live load are subjected to a reduction
when they act on a large tributary area since it is less likely that the entire large area will be loaded
to the same magnitude of high unit load. This reduction is not allowed when an added measure of
safety is desired for important structures.
Floor Live Loads
The floor live load is estimated by the equation
L = kLo
(2.1)
where
Lo is the basic design live load (see the “Basic Design live Load, L o” section below)
k is the area reduction factor (see the “Effective area reduction factor” section below)
Basic Design Live Load, Lo
The ASCE 7-05 provides a comprehensive table for basic design loads arranged by occupancy and
use of a structure. This has been consolidated under important categories in Table 2.1.
To generalize, the basic design live loads are as follows.
Above the ceiling storage areas: 20 psf; one or two family sleeping area: 30 psf; normal use
rooms: 40 psf; special use rooms (office, operating, reading, fixed sheet arena): 50–60 psf; public
assembly places: 100 psf; lobbies, corridors, platforms, and stadium*: 100 psf for first floor, 80 psf
for other floors; light industrial uses: 125 psf; and heavy industrial uses: 250 psf.
Effective Area Reduction Factor
The members that have more than 400 ft2 of influential area are subject to a reduction of the standard live loads. The influence area is defined as the tributary area, AT , multiplied by an element
factor, KLL , as listed in Table 2.2.
The following cases are excluded from the live load reduction:
1. Heavy live load that exceeds 100 psf
2.Passenger car garages
3.Public assembly areas
Except the above three items, for all other cases the reduction factor is given by
15
k = 0.25 +
K LL AT
(2.2)
* In addition to vertical loads, horizontal swaying forces as follows are applied to each row of sheets: 24 lb per linear ft of
seat in the direction to each row of sheets, and 10 lb per linear ft of sheet in the direction perpendicular to each row of
sheets. Both horizontal forces need not be applied simultaneously.
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Primary Loads: Dead Loads and Live Loads
Table 2.1
Summarized Basic Design Live Loads
Category
Uniform Load, psf
Residential
Storage area
Sleeping area (dwelling)
Living area, stairs (dwelling)
Hotel room
Garage
Office
Computer room/facility
School classroom
Hospital
Patient room
Operation room/lab
Library
Reading room
Stacking room
Industrial manufacturing/warehouse
Light
Heavy
Corridor/lobby
First floor
Above first floor
Public placesa
a
20
30
40
40
40
50
100
40
40
60
60
150
125
250
100
80
100
Balcony, ballroom, fire escape, gymnasium, public stairs/exits,
restaurant, stadium, store, terrace, theatre, yard, etc.
Table 2.2
Live Load Element Factor KLL
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Structure Element
KLL
Interior columns
Exterior columns without cantilever slabs
Edge columns with cantilever slabs
Corner columns with cantilever slabs
Edge beams without cantilever slabs
Interior beams
All other members not identified including
Edge beams with cantilever slabs
Cantilever beams
One-way slabs
Two-way slabs
Members without provisions for continuous shear
transfer normal to their span
4
4
3
2
2
2
1
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Principles of Structural Design: Wood, Steel, and Concrete
Joists
A
B
C
Beam
D
35 ft
60 ft
Figure 2.1 Floor framing plan.
As long as the following limits are observed, Equation 2.2 can be applied to any area. However with
the limits imposed, the factor k becomes effective when K LL AT > 400 as stated earlier:
1. k factor should not be more than 1.
2.k factor should not be less than 0.5 for members supporting one floor and 0.4 for members
supporting more than one floor.
Example 2.2
The first floor framing plan of a single family dwelling is shown in Figure 2.1. Determine the magnitude of the live load on the interior column C.
Solution
1. From Table 2.1, Lo = 40 psf
2. Tributary area AT = 20 × 17.5 = 350 ft 2
3. From Table 2.2, KLL = 4
4. KLL AT = 4 × 350 = 1400
5. From Equation 2.2,
15
k = 0.25 +
KLL AT
15
= 0.25 +
= 0.65
1400
6. From Equation 2.1, L = kLo = 0.65 (40) = 26 psf.
Other Provisions for Floor Live Loads
Besides the uniformly distributed live loads, the ASCE 7-05 also indicates the concentrated live
loads in certain cases that are assumed to be distributed over an area of 2.5 ft × 2.5 ft. The maximum
effect of either the uniformly distributed or concentrated load has to be considered. In most cases,
the uniformly distributed load controls.
The buildings where partitions are likely to be erected, a uniform partition live load is provided
in addition to the basic design loads. The minimum partition load is 15 psf. The partition live loads
are not subjected to reduction for large effective area.
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Primary Loads: Dead Loads and Live Loads
27
Live loads include an allowance for an ordinary impact. However, where unusual vibrations and
impact forces are involved, the live loads should be increased. The moving loads shall be increased
by an impact factor as follows: (1) elevator, 100%; (2) light shaft or motor-driven machine, 20%;
(3) reciprocating machinery, 50%; and (4) hangers for floor or balcony, 33%. Including these effects
Total LL/unit area = unit LL (1+ IF) + PL {min 15 psf}
(2.3)
where
LL is the live load
IF is the impact factor
PL is the partition load
Roof Live Loads, Lr
Roof live loads happen for a short time during the roofing or reroofing process. In the load combinations, either the roof live load Lr or the snow load S is included, since both of these are not likely to
occur simultaneously.
The standard roof live load for ordinary flat, sloped, or curved roofs is 20 psf. This can be reduced
to a minimum value of 12 psf based on the tributary area being larger than 200 ft2 and/or the roof
slope being more than 18.4°. When less than 20 psf of the roof live loads are applied to a continuous
beam structure, the reduced roof live load is applied to adjacent spans or to alternate spans, whichever produces the greatest unfavorable effect.
The roof live load is estimated by
Lr = R1R2 Lo
(2.4)
where
Lr is the reduced roof live load on a horizontally projected surface
L o is the basic design load for ordinary roof = 20 psf
R1 is the tributary area reduction factor, see the “Tributary Area Reduction Factor, R1” section
below
R2 is the slope reduction factor, see the “Slope Reduction Factor” section below
Tributary Area Reduction Factor, R1
This is given by
R1 = 1.2 − 0.001AT
(2.5)
where AT is the horizontal projection of roof tributary area in ft2.
This is subject to the following limitations:
1. R1 should not exceed 1
2.R1 should not be less than 0.6
Slope Reduction Factor
This is given by
R2 = 1.2 − 0.6 tan θ
(2.6)
where θ is the roof slope angle.
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Principles of Structural Design: Wood, Steel, and Concrete
1. R2 should not exceed 1
2.R2 should not be less than 0.6
Example 2.3
The horizontal projection of a roof framing plan of a building is similar to Figure 2.1. The roof pitch
is 7 on 12. Determine the roof live load acting on column C.
Solution
1. Lo = 20 psf
2. AT = 20 × 17.5 = 350 ft 2
3. From Equation 2.5: R1 = 1.2 – 0.001 (350) = 0.85
4. Pitch of 7 on 12, tan θ = 7/12 or θ = 30.256°
5. From Equation 2.6: R 2 = 1.2 − 0.6 tan 30.256° = 0.85
6. From Equation 2.4: Lr = (0.85) (0.85) (20) = 14.45 psf > 12 psf OK
The above computations are for an ordinary roof. Special purpose roofs such as roof gardens have
loads up to 100 psf. These are permitted to be reduced according to the floor live load reduction
as discussed in the “Floor Live Loads” section.
Problems
2.1 A floor framing consists of the following:
Hardwood floor (4 psf), 1 in. plywood (3 psf), 2 in. × 12 in. framing @ 4 in. on center (2.6 psf),
ceiling supports (0.5 psf), gypsum wallboard ceiling (5 psf).
Determine the floor dead load.
2.2In Problem 2.1, the floor covering is replaced by a 1 in. concrete slab and the framing by
2 in. × 12 in. at 3 in. on center. Determine the floor dead load.
[Hint: Weight of concrete/unit area = 1 ft × 1 ft × 1/12 ft × 150.]
2.3For the floor framing plan of Example 2.2, determine the design live load on the interior
beam BC.
2.4An interior steel column of an office building supports loads from two floors. The column-tocolumn distance among all columns in the floor plan is 40 ft. Determine the design live load
on the column.
2.5The framing plan of a light industrial building is shown in Figure P2.5. Determine the live
load on column A.
50 ft
50 ft
A
B
20 ft
20 ft
20 ft
Figure P2.5 Framing plan of a building.
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Primary Loads: Dead Loads and Live Loads
2.6 Determine the live load on the slab resting on column A of Problem 2.5.
2.7The building in Problem 2.5 includes partitioning of the floor and it is equipped with a reciprocating machine that induces vibrations on the floor. Determine the design live load on beam AB.
2.8Determine the roof live load acting on the end column D of a roofing plan shown in
Figure P2.8.
24 ft
B
A
C
D
24 ft sloped length
at pitch 6.3 to 10
20 ft
20 ft
20 ft
Purlins
Figure P2.8 Roofing plan.
2.9 Determine the roof live load on purlins of Figure P2.8 if they are 4 ft apart.
2.10A roof framing section is shown in Figure P2.10. The length of the building is 40 ft. The ridge
beam has supports at two ends and at mid-length. Determine roof live load on the ridge beam.
Ridge beam
2
1
Wall
30 ft
Figure P2.10 Side elevation of a building.
2.11 Determine the load on the walls due to roof live load of Problem 2.10.
2.12An interior column supports loads from a roof garden. The tributary area to the column is
250 ft2. Determine the roof live load. Assume a basic roof garden load of 100 psf.
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3 Snow Loads
Introduction
Snow is a controlling roof load in about half of all the states in the United States. It is a cause of
frequent and costly structural problems. Snow loads have the following components:
1. Balanced snow load
2.Extra load due to rain on snow
3.Partial loading of the balanced snow load
4.Unbalanced snow load due to a drift on one roof
5.Unbalanced load due to a drift from an upper to a lower roof
6.Sliding snow load
Snow loads are assumed to act on the horizontal projection of the roof surface.
Balanced Snow Load
This is the basic snow load to which a structure is subjected to. The procedure to determine the
balanced snow load is as follows:
1. Determine the ground snow load, pg, from the snow load map in the ASCE 7-05, reproduced in Figure 3.1.
2.Convert the ground snow load to flat roof snow load (roof slope ≤5°), pf , with consideration
given to the (1) roof exposure, (2) roof thermal condition, and (3) occupancy category of
the structure.
3.Apply a roof slope factor to the flat roof snow load to determine the sloped (balanced) roof
snow load.
4.Combining the above steps, the sloped roof snow load is calculated from
ps = 0.7CsCeCt Ipg
(3.1)
where
pg is the 50 year ground snow load from Figure 3.1
I is the importance factor (see the “Importance Factor” section)
Ct is the thermal factor (see the “Thermal factor, Ct” section)
Ce is the exposure factor (see the “Exposure Factor, Ce” section)
Cs is the roof slope factor (see the “Roof Slope Factor, Cs” section)
The slope of a roof is defined as a low slope if (1) it is a mono-slope roof having a slope of less
than 15°; (2) it is a hip and gable roof having a slope of less than (i) 2.4° or (ii) (70/W) + 0.5 whichever is higher, where W is the horizontal distance from eave to ridge of the roof in feet; and (3) it is
a curved roof having the vertical angle from the eave to crown of less than 10°.
31
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Principles of Structural Design: Wood, Steel, and Concrete
(200)
20
CS
(700)
20
(400)
15
CS
(1500)
20
(1500)
(2800) 15
20
(1000)
20
(800)
15
(600)
10
(400)
10
(300)
5
(500)
5
(300)
ZERO
(800)
5
(1800)
10
(1300)
5
(600)
ZERO
CS
CS
(2800)
5
(1800)
ZERO
(3600)
5
(2000)
ZERO
(1000)
ZERO
40
35
(6000)
25
(4500)
20
(6600)
15
CS
30
(6000)
35
(6000)
30
25
CS
(5200)
20
(4500)
15
(6300)
15
(5400)
10
(4500)
5
(3000)
ZERO
15
(5000)
10
(5000)
10
(4000)
5
(3500)
ZERO
(3000)
ZERO
20
(6200)
20
(6800)
15
(6400)
10
(6000)
5
CS
CS
(6000)
15
(4800)
5
(4000)
ZERO
In CS areas, site-specific case studies are required to
establish ground snow loads. Extreme local variations
in ground snow loads in these areas preclude mapping
at this scale.
Numbers in parentheses represent the upper elevation limits
in feet for the ground snow load values presented below.
Site-specific case studies are required to establish ground
snow loads at elevations not covered.
(6000)
10
(5000)
5
15
20
(6500)
15
(5000)
10
CS
(2000)
ZERO
50
(5500)
15
CS
(5400)
10
(4500)
5
(3000)
ZERO
CS
35
25
(4600)
15
(3800)
10
(5000)
15
(6000)
15
(4500)
10
(3600)
5
(2000)
ZERO
(2000)
5
(1500)
ZERO
(3700)
30
(4500)
20
(6500)
15
(4600)
10
(6400)
15
40
(3600)
20
(4800)
25
(4600)
20
(5400)
20
(5000)
10
(4000)
5
(2400)
ZERO
(4100)
25
60
35
(3000)
25
CS
CS
(3200)
20
50
(2600)
30
(6000)
15
(5000)
10
(4400)
10
(1500)
ZERO
(4600)
20
CS
(4300)
20
(4100)
15
(3200)
10
CS
(4000)
20
(3400)
15
(3300)
20
(1200)
10
(200)
10
(100)
5
20
20
(4400)
10
(3200)
5
CS
10
(3600)
10
(5000)
5
(3500)
ZERO
5
(4500)
ZERO
(3000)
ZERO
ZERO
2
To convert lb/sq ft to kN/m , multiply by 0.0479.
To convert feet to meters, multiply by 0.3048.
(a)
0
100
200
300 miles
Figure 3.1 Ground snow loads, pg, for the United States (lb/ft2). (Courtesy of American Society of Civil
Engineers, Reston, VA.)
For a low sloped roof, the magnitude of ps from Equation 3.1 should not be less than the
following values:
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1. When the ground snow load, pg, is 20 lb/ft2 or less, the minimum roof snow load for the
low-slope roof is given by
ps = Cs Ipg
(3.2)
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Snow Loads
(700)
100
70
50
90 100
50
60
70
70
60
50
(800)
60
60
CS
(500)
70
(1000)
60
CS CS
(500)
60
(700)
90
(1000)
40
40
40
(1000)
35
30
CS
(800)
35
(1700)
30
CS
25 (1200)
25
CS
25
CS
(900)
50
40
CS
50
35
40
35
30
(700)
50
25
35
(500)
50 (900)
50
35
30
(1700)
30
CS
(600)
80
30 25
25
25
20
20
20
25
20
(300)
30
(2500)
20
15
(2600)
15
CS
(2500)
25
25
20
5
15
(1800)
10
10
10
5
ZERO
5
ZERO
(b)
Figure 3.1 (continued)
2.When pg exceeds 20 lb/ft2, the minimum roof snow load for the low-slope roof is given by
ps = 20Cs I
(3.3)
Importance Factor
Depending upon the occupancy category identified in the “Classification of Buildings” section in
Chapter 1, the importance factor is determined from Table 3.1.
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Principles of Structural Design: Wood, Steel, and Concrete
Table 3.1
Importance Factor for Snow Load
Category of Occupancy
Importance Factor
I. Structures of low hazard to human life
II. Standard structures
III. High occupancy structures
IV. Essential structures
0.8
1.0
1.1
1.2
Source: Courtesy of American Society of Civil Engineers,
Reston, VA.
Thermal Factor, Ct
The factors are given in Table 3.2. The intent is to account for the
heat loss through the roof and its effect on snow accumulation. For
modern, well-insulated, energy-efficient construction with eave
and ridge vents, the common Ct value is 1.1.
Exposure Factor, Ce
Table 3.2
Thermal Factor for Snow
Load
Thermal Condition
Green house with interior
temperature of at least 50°
Well above freezing (warm
or hot) roofs
Just above freezing or
well-insulated, ventilated
roofs
Below freezing structure
Ct
0.85
1.0
1.1
The factors, as given in Table 3.3, are a function of the surface
roughness (terrain type) and the location of the structure within the
terrain (sheltered to fully exposed).
1.2
It should be noted that Exposure A representing centers of large
cities where over half the buildings are in excess of 70 ft is not
recognized separately in the ASCE 7-05. This type of terrain is
included into Exposure B.
The sheltered areas correspond to the roofs that are surrounded on all sides by the obstructions
that are within a distance of 10ho, where ho is the height of the obstruction above the roof level. Fully
exposed roofs have no obstruction within 10ho on all sides including no large roof top equipment
Table 3.3
Exposure Factor for Snow Load
Terrain
B. Urban, suburban wooded
C. Open, flat open grasslands,
water surfaces in hurricane-prone
regions
D. Open, smooth mud and salt
flats, water surfaces in
non-hurricane-prone regions
Above the tree line in
mountainous region
Alaska: treeless
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Fully
Exposed
Partially
Exposed
Sheltered
0.9
0.9
1.0
1.0
1.2
1.1
0.8
0.9
1.0
0.7
0.8
—
0.7
0.8
—
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