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? | ||

Air Conditioned Building? | ||

Fixed Base Columns? | ||

Vastly Uneq. End Stiff.? |

#### Result :

Determine Max. Design Temperature Change, DT, per Ref. #1: | |||||||
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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. |
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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: | ||
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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.

‘Calculations courtesy of Alex Tomanovich, PE ’ |
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