expansion joints - when where and how

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EXPANSION JOINTS: WHERE, WHEN AND HOW JAMES M. FISHER  James M. Fisher  Biography James M. Fisher is vice president of Computerized Structural Design (CSD), a Milwaukee, Wisconsin, consulting engineering firm. He received a Bachelor of Science degree in civil engineering fr om the University of Wisconsin in 1962. After serving two years as a Lieutenant in the United States Army Corps of Engineers, he continued his formal education. He received his Master of Science and Ph.D. degree in s tructural engineering from the University of Illinois in 1965 and 1968 respectively. Prior to joining CSD, he was an ass istant professor of structural engineering at the University of Wisconsin a t Milwaukee. He is a registered structural e ngineer in several states. Fisher has specialized in structural steel research and development. He has spent a large part of his career investigating building systems and the study of economical structural framing systems. He was a former chairman of the American Society of Civil Engineers Committee on the Design of Steel Building Structures. Fisher is a member of the American Iron and Steel Institute (AISI) Committee on Specifications, and a member of the AISC Specification Committee for the Design Fabrication and Erection of Structural Steel Buildings. Fisher is the co- author of seven books, as well as the author of many technical publications in the field of structural engineering. He is a member of the American Society of Civil Engineers and honorary fraternities Tau Beta Pi, Sigma Xi, Chi Epsilon and Phi Kappa Phi. Fisher received the 1984 T.R. Higgins Lectureship Award presented by the American Institute of Steel Construction. Abstract This presentation will address means of determining where building expansion joints should be located within a structure. When expansion joints are required, a nd how to pr oportion and design ap propriate joints. Expansion  joints for commercial as well as industrial facilities will be discusse d. Details of various types of joints will be presented. 

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EXPANSION JOINTS: WHERE, WHEN AND HOW 

JAMES M. FISHER

 James M. Fisher  

BiographyJames M. Fisher is vice president of Computerized Structural Design (CSD), a Milwaukee, Wisconsin, consultingengineering firm. He received a Bachelor of Science degree in civil engineering from the University of Wisconsinin 1962. After serving two years as a Lieutenant in the United States Army Corps of Engineers, he continued hisformal education. He received his Master of Science and Ph.D. degree in structural engineering from the University

of Illinois in 1965 and 1968 respectively. Prior to joining CSD, he was an assistant professor of structuralengineering at the University of Wisconsin at Milwaukee. He is a registered structural engineer in several states.Fisher has specialized in structural steel research and development. He has spent a large part of his careerinvestigating building systems and the study of economical structural framing systems. He was a former chairman of the American Society of Civil Engineers Committee on the Design of Steel Building Structures. Fisher is a memberof the American Iron and Steel Institute (AISI) Committee on Specifications, and a member of the AISCSpecification Committee for the Design Fabrication and Erection of Structural Steel Buildings. Fisher is the co-author of seven books, as well as the author of many technical publications in the field of structural engineering.He is a member of the American Society of Civil Engineers and honorary fraternities Tau Beta Pi, Sigma Xi, ChiEpsilon and Phi Kappa Phi. Fisher received the 1984 T.R. Higgins Lectureship Award presented by the AmericanInstitute of Steel Construction. 

AbstractThis presentation will address means of determining where building expansion joints should be located within a

structure. When expansion joints are required, and how to proportion and design appropriate joints. Expansion joints for commercial as well as industrial facilities will be discussed. Details of various types of joints will bepresented. 

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EXPANSION JOINTS: WHERE WHEN AND HOW

JAMES M. FISHER1 

IntroductionIn the most basic sense the need for an expansion joint in a structure depends on the consequence of not having anexpansion joint. Will the lack of an expansion joint hamper or destroy the function of the facility, or cause damageto the structural or architectural components? The number and location of building expansion joints is a designissue not fully treated in technical literature. The LRFD Specification (AISC, 1999) lists expansion and contractionas a serviceability issue and provides the statement in Section L2, “Adequate provision shall be made for expansionand contraction appropriate to the service conditions of the structure.”

ASCE 7-02 “Minimum Design Loads for Buildings and Other Structures” (ASCE, 2002) states, “Dimensionalchanges in a structure and its elements due to variations in temperature, relative humidity, or other effects shall notimpair the serviceability of the structure.”

This paper will focus on the basic requirements used to determine if an expansion joint is required at a givenlocation, or locations within a structure. Requirements of expansion joints as they pertain to commercial, industrial

and long span structures are discussed. Area dividers as provided in roof membranes to control the effects of thermal loads for roofing are not discussed, as they are relief joints in the membrane and do not require a joint in theroof structure below.

General RequirementsAlthough buildings are often constructed using flexible materials, roof and structural expansion joints are requiredwhen plan dimensions are large. It is not possible to state exact requirements relative to distances betweenexpansion joints because of the many variables involved, such as, ambient temperatures during construction and theexpected temperature range during the life of a building. The National Roofing Contractors Association (NRCA,2001) gives the following recommendations for the location of roof expansion joints:

• Where steel framing, structural steel, or decking change direction.

• Where separate wings of L, U, T shaped buildings or similar configurations exist.

• Where the type of decking changes, for example, where a precast concrete deck and a steel deck abut.

• Where additions are connected to existing buildings.

• At junctions where interior heating conditions change, such as a heated office abutting unheatedwarehouse, canopies, etc.

• Where movement between walls and the roof deck may occur.

It should be noted that the NRCA standard details show that the roof structure under roof expansion joints isintended to be discontinuous.

The Building Research Advisory Board of the National Academy of Sciences (NAS, 1974) published FederalConstruction Council Technical Report No. 65 “Expansion Joints in Buildings” (No longer in print). The reportpresents the graph shown in Figure 1 as a guide for spacing expansion joints in beam and column frame buildings asa function of design temperature change. The graph is directly applicable to buildings of beam and column

construction, hinged at the base, and with heated interiors. When other conditions prevail, the following rules areapplicable:

1. If the building will be heated only and will have hinged-column bases, use the allowable length asspecified;

2. If the building will be air conditioned as well as heated, increase the allowable length by 15 percent(provided the environmental control system will run continuously);

3. If the building will be unheated, decrease the allowable length by 33 percent;

1James M. Fisher is Vice President Computerized Structural Design, S.C., Milwaukee, WI

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4. If the building will have fixed column bases, decrease the allowable length by 15 percent;5. If the building will have substantially greater stiffness against lateral displacement at one end of the plan

dimension, decrease the allowable length by 25 percent.

When more than one of these design conditions prevails in a building, the percentile factor to be applied should bethe algebraic sum of the adjustment factors of all the various applicable conditions.The report also includes temperature data for numerous cities. This data is reprinted in Appendix B of this paper.

Tw, is the temperature exceeded only 1% of the time during summer months, Tm, the mean temperature during thenormal construction season and T

c, the temperature exceeded 99% of the time during winter months. The design

temperature change is the larger of the two temperatures differences either (Tw-T

m) or (T

m-T

c).

Fig. 1 Expansion Joint Spacing Graph[Taken from F.C.C. Tech. Report No. 65,

 Expansion Joints in Buildings]

Rather than consulting the above values, many engineers use a temperature change of 50 to 70 degrees for enclosedheated / air-conditioned buildings.

In equation form the NAS requirements given above can be shown as follows:

( )max 1 2 3 4L allow allow L R R R R L= + − − − (Eq. 1)

where:

Lmax

= Maximum length of a building with no expansion joints or between expansion joints.R

1= 0.15, if the building is heated and air-conditioned.

R2

= 0.33, if the building is unheated.

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R3

= 0.25, if columns are fixed base.R

4= 0.25, if the building has substantially greater stiffness at one end.

Lallow

= Allowable length from Fig. 1

As a general rule expansion joints should always be carried through the roofing membrane.

Regarding the type of structural expansion joint, most engineers agree that the best expansion joint (and generally

the most expensive) is to use a line of double columns to provide a complete separation in the building frame at the joints. When joints other than the double column type are employed, low friction sliding elements, such as Teflonpads are used between the faying surfaces. It should be remembered that slip connections are not totally frictionless.In addition, they may induce some level of restraint to movement due to binding or debris build-up.

Very often buildings may be required to have fire walls in specific locations. Fire walls may be required to extendabove the roof or they may be allowed to terminate at the underside of the roof. Such fire walls become locationsfor expansion joints. In such cases the detailing of joints can be difficult because the fire wall must be supportedlaterally.

Figure 2 depicts typical details to permit limited expansion. Additional details are given in various architecturaltexts. Not shown in the joist details is the OSHA bolting requirements that may be necessary.

The designer is also cautioned that when roof diaphragm forces are to be transferred into shear walls or vertical X-bracing systems the transfer should be accomplished mid-way between expansion joints allowing edge members toexpand and contract freely away from the fixed point of resistance.

Expansion Joint SizeThe width of an expansion joint is determined from the basic thermal expression for the material used for the frames

in the structure, ∆ = αL∆T. Where α =0.0000065 for steel structures, L is the length subject to the temperature

change, and ∆T

is the temperature change.

∆T

is based on the design temperature change, (Tw-T

m) or (T

m-T

c). The change during the construction cycle, (T

m-T

c),

is usually the largest.

Structural Roof SystemsMetal roofs are of two types: Through Fastener Roofs (TFR) and Standing Seam Roofs (SSR). Standing SeamRoofs for the purpose of this discussion include only those of the floating type. Standing seam roofs without thefloating feature should be treated as Through Fastener Roofs.

Through fastener roofs rely on purlin roll to prevent slotting of the roof panels and to relieve thermal force build-up.Because of their greater lateral seat stiffness steel joists should not be used with through fastener roofs, except inrare instances such as small roofs. A practical limit between expansion joints for TFR is in the range of 100 to 200feet, when these roofs are attached to light gage cold-formed purlins.

Standing seam roofs are limited by the range of the sliding clips. Depending on the manufacturer, it is in the range of 150 to 200 feet.

Standing seam roofs are more flexible in the direction perpendicular to the ribs, as compared to the direction of theribs, thus expansion joints can be spaced at greater distances than those perpendicular to the ribs. The roof manufacturer’s recommendations should be consulted and followed relative to the distances between expansion joints.

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Overhead Crane Buildings

Vertical Bracing

Vertical bracing for wind, seismic, or crane longitudinal runway forces should be located at or near the center of therunway length. Expansion and contraction can then occur away from the brace location. This will help prevent the

permanent elongation of the vertical bracing due to temperature changes. The disadvantage of the center placementof the bracing is that bumper forces has to be transferred a greater distance to get to the bracing as compared tobraces that are located near the crane stops.

Crane Runway BeamsOnly as a last resort should expansion joints are provided for runway beams. By providing oversize holes at thebeam ends expansion and contraction can be allowed in each beam segment, so that an expansion joint is notnecessary. If an expansion joint is provided in the runway system, careful consideration must be given as to how thelateral crane forces are transferred across the joint. Special details are required to prevent high shears in the cranerail, and large forces in the rail clamps.

Crane RailsExpansion joints should never be provided in the crane rails. Such joints often lead to rail cracking. In lieu of such joints, the rail should be allowed to expand toward the stops. Adequate space must be allowed between the end of the rail and the face of the crane stops. In addition, a rail clamping system which allows longitudinal expansion andcontraction of the rail must be provided, particularly in runway systems which exceed 400 ft. in length.

Large Clear Span StructuresLong span structures and components often require special expansion joint hardware. The majority of bearings onlyhave expansion and contraction capabilities of plus or minus one inch. Bearings which have smooth stainless steelsurfaces can be specified for much grater expansion and contraction amounts. Slide bearings generally have acoefficient of frictions from 0.04 to 0.08. The bearings can accommodate pressures from 2000 to 4000 psi.Manufactures of slide bearings can be found on the web. The manufacturer should be consulted for proper orderingand installation procedures.

Special DetailsOn occasion special expansion joint details are required to transfer shear across the expansion joint, two such detailsare shown in Figures 3 and 4. In Figure 3 the strapping is relatively flexible thus allowing expansion andcontraction across the joint, and yet is stiff in the direction perpendicular to the joint thus allowing shear transfer.The joint shown in Figure 4 allows shear transfer through bearing.

Construction ConcernsThe author has experienced several issues relative to construction difficulties associated with expansion joints. Thefirst is that temperature changes to which an unenclosed unheated structure is subjected to during construction mayexceed the design temperature changes after completion of the structure. These increased temperature changesshould be considered by the designer. The temperature to be considered during construction, of course, varies

depending upon building location. Engineers often use a maximum value of 70 degrees for calculation purposes. Amore accurate value to use is the T

m-T

cvalue from the NAS Report.

Sometimes it is very difficult for the steel erector to adjust the expansion joint at the desired location as normalerection tolerances may force the expansion joint to one end of its travel. This problem can be eliminated if thedesigner considers a detail at the far end of the member to which the expansion joint is located, as a means of adjustment. In this way the construction tolerance can be compensated.

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Sheet Metal CapBatt Insulation

2 x 10 Continuous

Wood Cant

Wood NailerBolt or Screw toJoist or Deck

Do Not WeldThis Side

"A"

Do Not Weld

Bent Bar

SECTION "A"

Typ.

Low Friction SlidingElement (Optional)

Wood Nailer-Screw to Deck

Built-up RoofingSteel Deck

Insulation

Do Not WeldThis Side

Sheet Metal Cap

Batt Insulation

2 x 10 Continuous

Wood Cant

Joist

PurlinSlotted Holes in P.Tighten Bolts FingerTight, Provide JambNut or T.W. Bolt toNut, Provide Washers

L

Fig. 2 Typical Expansion Joints 

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Fig. 3 Shear Across Expansion Joint 

BRACING SAG SUPPORT

CONNECT TO ONE SIDE

ONLY

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 Fig. 4 Shear Across Expansion Joint 

Example 1: 400 Foot Long Braced Frame

Determine whether a rectangular 400 ft. by 180 ft., unheated building with pinned base columns requires anexpansion joint. The building has x-bracing at one end only in the two side walls along the 400 ft. direction. Thebuilding is located in Buffalo, New York.

From the Appendix: For Buffalo, New York: Tw

= 88, Tm

= 59, Tc= 3

 Design Temperature Change = Maximum of (Tw-T

m)or (T

m-T

c) = Maximum of (88-59) or (59-3) = 56 degrees

From Equation (1): ( )max 1 2 3 4L allow allow L R R R R L= + − − −  

Where:

R1 = 0.15, the building is not heated and nor air-conditioned, N.A.R

2= 0.33 the building is unheated.

R3

= 0.25 the columns are fixed base, N.A.R

4= 0.25 the building has substantially greater stiffness at one end.

From Fig. 1: Lallow

= 450 ft.

( )( )maxL 450 0 0.33 0 0.25 450 189= + − − − = ft.

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Therefore an expansion joint is required. Since the building is a braced frame and the bracing is at only one end of atypical frame additional bracing will be required on both sides of the expansion joint.

Example 2: Expansion Joint Size

Determine the size of the expansion joint required for the building in Example 1. The structure is braced at both

ends away from the expansion joint.

∆ = 0.0000065L∆T

= (2)(0.00065)(200)(56/100) = 0.146 ft. = 1.75 in., USE 2 in. total movement.

The above calculation assumes that the thermal movement for each segment occurs away from the x-braced bays.

REFERENCESAmerican Institute of Steel Construction, 1999, Load and Resistance Factor Design Specification for Structural 

Steel Buildings and Commentary, Chicago, IL.

American Society of Civil Engineers, 2003, Minimum Design Loads for Buildings and Other Structures, ASCE 7-02, ASCE Reston, VA.

Federal Construction Council, 1974, Technical Report No. 65, 1974, Expansion Joints in Buildings, NationalResearch Council, Washington, D.C. (out of print)

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APPENDIX B

TEMPERATURE DATA

The following tabulation presents mean construction season temperature (Tm) and extreme summer (T

w) and winter

(Tc) temperature data for various localities in the United States. Most stations listed are located at airports; those

identified as CO are city offices.

Tm

= the mean temperature during the normal construction season in the locality of the building. For thepurpose of this report the normal construction season for a locality is defined as that contiguous period in

a year during which the minimum daily temperature equals or exceed 32°F.* 

Tw

= the temperature exceeded, on the average, only 1 percent of the time during the summer months of Junethrough September in the locality of the building. (In a normal summer there would be approximately 30hours at or above the design value.

**)

Tc

= the temperature equaled or exceeded, on the average, 99 percent of the time during the winter months of December, January, and February in the locality of the building. (In a normal winter there would beapproximately 22 hours at or below this design value.

**)

*These contiguous periods for each locality in the United States were obtained from the Decennial Census of United

States Climate: Daily Normals of Temperature and Heating Degree Days (see reference on page 11) and the meanconstruction season temperature values T

mwere computed (by Maj. T.E. Stanton of the USAF Environmental

Technical Applications Center, Washington, D.C.) from the mean monthly temperatures extracted from the NationalWeather Services’ Local Climatological Data Summaries for the stations. In a few cases other sources also wereused.

**The T

wand T

cvalues are extracted from the ASHRAE Handbook of Fundamentals (1972), published by the

American Society of Heating, Refrigerating and Air Conditioning Engineers.

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Temperature (°F) Temperature (°F)Station

Tw

Tm

Tc 

StationT

wT

mT

Alabama Florida (Continued)Birmingham 97 63 19 Jacksonville 96 68 29Huntsville 97 61 13 Key West 90 77 55Mobile (CO) 96 68 28 Lakeland (CO) 95 72 35Montgomery 98 66 22 Miami 92 75 44

Miami Beach (CO) 91 75 45Alaska Orlando 96 72 33

Anchorage 73 51 -25 Pensacola (CO) 92 68 29Barrow 58 38 -45 Tallahassee 96 68 25Fairbanks 82 50 -53 Tampa 92 72 36Juneau 75 48 -7 West Palm Beach 92 75 40Nome 66 45 -32

GeorgiaArizona Athens 96 61 17

Flagstaff 84 58 0 Atlanta 95 62 18Phoenix 108 70 31 Augusta 98 64 20Prescott 96 64 15 Columbus 98 65 23Tucson 105 67 29 Macon 98 65 23

Winslow 97 67 9 Rome 97 62 16Yuma 111 72 37 Savannah/Travis 96 67 24

Arkansas HawaiiFt. Smith 101 65 15 Hilo 85 73 59Little Rock 99 65 19 Honolulu 87 76 60Texarkana 99 65 22

Idaho California Boise 96 61 4

Bakersfield 103 65 31 Idaho Falls 91 61 -12Burbank 97 64 36 Lewiston 98 60 6Eureka/Arcata 67 52 32 Pocatello 94 60 -8Fresno 101 63 28Long Beach 87 63 41 Illinois

Los Angeles 94 62 41 Chicago 95 60 -3Oakland 85 57 35 Moline 94 63 -7Sacramento 100 60 30 Peoria 94 61 -2San Diego 86 62 42 Rockford 92 62 -7San Francisco 83 56 35 Springfield 95 62 -1Santa Maria 85 57 32

IndianaColorado Evansville 96 65 6

Alamosa 84 60 -17 Fort Wayne 93 62 0Colorado Springs 90 61 -1 Indianapolis 93 63 0Denver 92 62 -2 South Bend 92 61 -2Grand Junction 96 64 8Pueblo 96 64 -5 Iowa

Burlington 95 64 -4Connecticut Des Moines 95 64 -7

Bridgeport 90 60 4 Dubuque 62 63 -11Hartford 90 61 1 Sioux City 96 64 -10New Haven 88 59 5 Waterloo 91 63 -12

Delaware KansasWilmington 93 62 12 Dodge City 99 64 3

Goodland 99 65 -2

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Temperature (°F) Temperature (°F)Station

Tw

Tm

Tc 

StationT

wT

mT

Florida Topeka 99 69 3Daytona Beach 94 70 32 Wichita 102 68 5Ft. Myers 94 74 38

Kentucky MontanaCovington 93 63 3 Billings 94 60 -10Lexington 94 63 6 Glasgow 96 60 -25Louisville 96 64 8 Great Falls 91 58 -20

Havre 91 58 -22Louisiana Helena 90 58 -17

Baton Rouge 96 68 25 Kalispell 88 56 -7Lake Charles 95 68 29 Miles City 97 62 -19New Orleans 93 69 32 Missoula 92 58 -7Shreveport 99 66 22

NebraskaMaine Grand Island 98 65 -6

Caribou 85 56 -18 Lincoln (CO) 100 64 -4Portland 88 58 -5 Norfolk 97 64 -11

North Platte 97 64 -6Maryland Omaha 97 64 -5

Baltimore 94 63 12 Scottsbluff 96 62 -8Frederick 94 63 7

NevadaMassachusetts Elko 94 61 -13

Boston 91 58 6 Ely 90 59 -6Pittsfield 86 58 -5 Las Vegas 108 66 23Worcester 89 58 -3 Reno 95 62 2

Winnemucca 97 63 1Michigan

Alpena 87 57 -5 New HampshireDetroit-Metropolitan 92 58 4 Concord 91 60 -11Escanaba 82 55 -7

Flint 89 60 -1 New JerseyGrand Rapids 91 62 2 Atlantic City 91 61 14Lansing 89 59 2 Newark 94 62 11Marquette 88 55 -8 Trenton (CO) 92 61 12Muskegon 87 59 4Sault Ste Marie 83 55 -12 New Mexico

Albuquerque 96 64 14Minnesota Raton 92 64 -2

Duluth 85 55 -19 Roswell 101 70 16International Falls 86 57 -29Minneapolis/St. Paul 92 62 -14 New York Rochester 90 60 -17 Albany 91 61 -5St. Cloud 90 60 -20 Binghamton (CO) 91 67 -2

Buffalo 88 59 3Mississippi New York 94 59 11

Jackson 98 66 21 Rochester 91 59 2Meridian 97 65 20 Syracuse 90 59 -2Vicksburg (CO) 97 66 23

North CarolinaMissouri Asheville 91 60 13

Columbia 97 65 2 Charlotte 96 60 18Kansas City 100 65 4 Greensboro 94 64 14St. Joseph 97 66 -1 Raleigh/Durham 95 62 16

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Temperature (°F) Temperature (°F)Station

Tw

Tm

Tc 

StationT

wT

mT

St. Louis 98 65 4 Wilmington 93 63 23Springfield 97 64 5 Winston/Salem 94 63 14

North Dakota TennesseeBismarck 95 60 -24 Bristol/Tri City 92 63 11Devils Lake 93 58 -23 Chattanooga 97 60 15Fargo 92 59 -22 Knoxville 95 60 13Minot 91 ? -24 Memphis 98 62 17Williston 94 59 -21 Nashville 97 62 12

Ohio TexasAkron/Canton 89 60 1 Abilene 101 65 17Cincinnati (CO) 94 62 8 Amarillo 98 66 8Cleveland 91 61 2 Austin 101 68 25Columbus 92 61 2 Brownsville 94 74 36Dayton 92 61 0 Corpus Christi 95 71 32Mansfield 91 61 1 Dallas 101 66 19Sandusky (CO) 92 60 4 El Paso 100 65 21

Toledo 92 61 1 Fort Worth 102 66 20Youngstown 89 59 1 Galveston 91 70 32

Houston 96 68 28Oklahoma Laredo AFB 103 74 32

Oklahoma City 100 64 11 Lubbock 99 67 11Tulsa 102 65 12 Midland 100 66 19

Port Arthur 94 69 29Oregon San Angelo 101 65 20

Astoria 79 50 27 San Antonio 99 69 25Eugene 91 52 22 Victoria 98 71 28Medford 98 56 21 Waco 101 67 21Pendleton 97 58 3 Wichita Falls 103 66 15Portland 91 52 21Roseburg 93 54 25 Utah

Salem 92 52 21 Salt Lake City 97 63 5

Pennsylvania VermontAllentown 92 61 3 Burlington 88 57 -12Erie 88 59 7Harrisburg 92 61 9 VirginiaPhiladelphia 93 63 11 Lynchburg 94 62 15Pittsburgh 90 63 5 Norfolk 94 60 20Reading (CO) 92 61 6 Richmond 96 64 14Scranton/Wilkes-Barre 89 61 2 Roanoke 94 63 15Williamsport 91 61 1

Washington, D.C.Rhode Island National Airport 94 63 16

Providence 89 60 6Washington

South Carolina Olympia 85 51 21Charleston 95 66 23 Seattle 85 51 20Columbia 98 64 20 Spokane 93 58 -2Florence 96 64 21 Walla Walla 98 57 12Greenville 95 61 19 Yakima 94 62 6Spartanburg 95 60 18

West Virginia

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Temperature (°F) Temperature (°F)Station

Tw

Tm

Tc 

StationT

wT

mT

South Dakota Charleston 92 63 9Huron 97 62 -16 Huntington (CO) 95 63 10Rapid City 96 61 -9 Parkersburg (CO) 93 62 8Sioux Falls 95 62 -14

Wisconsin WyomingGreen Bay 88 59 -12 Casper 92 59 -11La Crosse 90 62 -12 Cheyenne 89 58 -6Madison 92 61 -9 Lander 92 58 -16Milwaukee 90 60 -6 Sheridan 95 59 -12