# Thermal Effects for Steel Buildings & Structures Calculator

Determine Max. Design Temperature Change, Change of Length or Stress as Applicable,
and Max. Length either without or between Expansion Joints

#### Input Data

 Summer Temp., Tw = o F Mean Temp., Tm = o F Winter Temp., Tc = o F Length, L = ft Heated Building? Yes No Air Conditioned Building? Yes No Fixed Base Columns? No Yes Vastly Uneq. End Stiff.? No Yes

#### Result :

Determine Max. Design Temperature Change, DT, per Ref. #1:
Temp. Change, DT1 = o F DT1 = Tw-Tm
Temp. Change, DT2 = o F DT2 = Tm-Tc
Maximum Design DT = o F DT = Maximum of: DT1 or DT2
For Unrestrained Condition, Calculate Change of Length Due to Temperature Change:
Thermal Exp. Coef., a = in./in./ o F a = Coefficient of thermal expansion for steel (from Ref. #2)
DL = in. DL = a*DT*(L*12) = s*(L*12)/E = F*(L*12)/(A*E) where: s = F/A
For Restrained Ends, Calculate Change in the Unit Stress Due to Temperature Change:
Mod. of Elasticity, E = ksi E = 29000 (assumed modulus of elasticity for steel)
Thermal Exp. Coef., a = in./in./ o F a = Coefficient of thermal expansion for steel (from Ref. #2)
Stress Change, Ds = ksi Ds = a*E*DT
Determine Max. Building or Structure Length either without or between Expansion Joints:
(from Ref. #1, Figure 1) for: DT <= 25, L(allow) = 600 ft.
Length, L(allow) = ft. for: 25 < DT > 70, L(allow) = -(200/45)*Dt+(600+25*(200/45)) ft.
for: DT >= 70, L(allow) = 400 ft.
R1 =   R1 = +0.15 if building is heated and air-conditioned, else 0
R2 =   R2 = -0.33 if building is unheated, else 0
R3 =   R3 = -0.15 if columns are fixed base in length direction, else 0
R4 =   R4 = -0.25 if bldg. has vastly greater stiffness at one end, else 0
Length, L(max) = ft. L(max) = L(allow)*(1+(R1+R2+R3+R4))

References:
1. "Expansion Joints in Buildings" - Technical Report No. 65
by: Federal Construction Council for National Academy of Sciences, 1974
2. Steel Construction Manual - 13th Edition (pages 2-31 to 2-33 and page 17-23)
by: American Instritute of Steel Construction (AISC), 2005
3. "Expansion Joints: Where, When and How"
by: James M Fisher, S.E. - published in Modern Steel Construction Magazine, April 2005

FIGURE 1:
Maximum allowable building length without use of expansion joints for various design temperature changes. This curve is directly applicable to steel buildings of beam-and- column construction, hinged at base, and with heated interiors. When other conditions prevail, the following rules are applicable:

(a) If the building will be heated only and will have hinged-column bases, use the allowable length as specified.
(b) If the building will be air conditioned as well as heated, increase the allowable length by 15% (provided the environmental control system will run continuously).
(c) If the building will be unheated, decrease the allowable length by 33%.
(d) If the building will have fixed-column bases, decrease the allowable length by 15%.
(e) If the building will have substantially greater stiffness against lateral displacement at one end of the plan dimension, decrease the allowable length by 25%.

Note: When more than one of these design conditions prevail in a building, the percentile factor to be applied should be the algebraic sum of the adjustment factors of all of the various applicable conditions.

Reference: "Expansion Joints in Buildings" - Technical Report No. 65 by: Federal Construction Council for National Academy of Sciences, 1974 (Note: Figure 1 from above reference is same as Figure 2-6 from AISC 13th Ed. Manual.)

Convert oC to oF:
oC =
oF = oF = (9/5)*(oC)+32

Vertical Bracing Locations when Considering Thermal Effects

Option #1:
Poor - Limits ability to expand/contract since ends are restrained, thus locking in thermal stresses.

Option #2:
Better - Provides ability to expand/contract in one direction only.

Option #3:
Best - Provides ability to expand/contract from middle in both directions.

Disclaimer: This calculator is not intended to be used for the design of actual structures, but only for schematic (preliminary) understanding of structural design principals. For the design of an actual structure, a competent professional should be consulted.

‘Calculations courtesy of Alex Tomanovich, PE ’