07 thermal stress

8/12/2019 07 Thermal Stress

1/13

Thermal stress and strain Prof Schierle 1

Therma l Stress St ra in


2/13


Therma l Stress St ra in


3/13


Thermal Stress & Strain

Thermal stress and strain are caused by

temperature change.

Materials expand at temperature increase

and contract at temperature decrease.

Restricting thermal strain cause thermal stress.

Thermal stress / strain are shown at left

1. Wall (bending stress)2. Moment frame (bending stress)

3. Braced frame (axial stress)

4. Fixed-end arch (bending stress)

5. Pin supported arch (bending stress)6. Three-hinge arch (no stress)

The three-hinge arch is free to deform

without stress (important advantage!)


4/13


Three-hinge arch

Many 19th century rail stations havethree-hinge arches to avoid thermal

stress and stress due to settlement.

The hinges also facilitate transport.


5/13


Three-hinge arch

Grimshaws Waterloo Station, London,

has three-hinge arches to avoid thermal stress

and settlement stress.

The asymmetrical form due to planning constrains

required to brace arches against buckling by

trusses located: Outside to prevent upward buckling

Inside to prevent downward buckling.

Hinges


6/13Thermal stress and strain Prof Schierle 6

Thermal strain

1 Bar of initial length L2 Thermal strainL due to heat,

computed as:

L = t Lwhere

= Coefficient of thermal expansion (in/in/oF)

t = temperature increase (+) / decrease (-)

L = initial length


7/13



Thermal Stress

3. Bar of initial length L

4. ElongationL due to heat

5. Hot bar reduced to initial length by load P

6. Thermal stress in restrained bar

L = t LL/L = t

=L/L

= t

E = f / f = E

f = t Ewhere

f = thermal stress

= thermal coefficient

t = temperature change

E = elastic modulus



Curtain wall

Assume:

Aluminum curtain wall Fa = 10 ksi

t = 100oF (summer vs.wintertemperature)2 story mullion, L = 30 x 12 L = 360

= 13 x 10-6 in/in/oF

E = 10 x 106 psi

Expansion joint

L = t L

L = 13 x 10-6 x 100o x 360 L = 0.47

Use expansion joint 0.5 > 0.47, ok

Assume:

Designer forgets expansion joint

Thermal stress:

f = t E

f = 13x10-6x100x10x106 = 13,000 psi

f = 13,000 psi / 1000 f = 13 ksi

13 > 10, NOTok

Note:106 and 10-6 cancel out and can be ignored



Masonry expansion joint

Silicon joint

L

1

2

34

1 Building axon

2 Expansion joint in wall

3 Expansion joint at wall intersection4 Expansion joint detail

Space masonry expansion joint @ L = 100

Assume:Masonry Fa = 300 psi

Temperature change t = 70oF

Joint spacing L=100 x 12 L = 1200

Thermal coefficient = 4x10-6/oF

E-modulus E = 1.5x106psi

Thermal expansion

L = t L

L = 4x10

-6

/

o

Fx70

o

x1200

L = 0.34Use 3/8 expansion joint 0.375 > 0.34

Check thermal stress without expansion joint

f = t E

f = 4x10-6

x70o

x1.5x106

f = 420psi420 > 300, NOT ok



Bridge expansion jointsBridges require expansion joints (roller or rocker)

AssumeConcrete bridge

Span L = 310 x 12 L =3,720

Temperature change t = 90oF

Thermal coefficient = 6x10-6/oFE-modulus E = 3x106psi

Thermal strain

L = t LL = 6x10-6x90ox3720 L = 2

Provide 2 joint 2.5 > 2

Thermal stress without jointf = t E

f = 6x10-6x90ox3x106psi f = 1,620 psi

Too much stress without load



Girder strainIIT Building Chicago

Architect: Mies Van der Rohe

Roof girders are exposed to temperature

change (cold winter / hot summer)

Assume

Steel girders

Span L= 120 x 12 L =1,440

Temperature change

t = 107o

Thermal coefficient =6.5x10-6/oF

E-modulus E = 29x106psi

Girder strain

L = 6.5x10-6x107ox1440 L = 1

Note:

girder elongation induces bending stress and

deflection in columns

07 thermal stress

Documents