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Chapter 2. Primary Loads: Dead Loads and Live Loads

Chapter 2. Primary Loads: Dead Loads and Live Loads

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24



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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25



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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26



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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28









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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29



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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32



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:









73397_C003.indd 32



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)



6/18/2010 3:17:40 PM



33



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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34



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



73397_C003.indd 34



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







6/18/2010 3:17:41 PM



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