Thermal Stress & Strain. 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 3

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1 Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 3

2 Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 4

3 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!) 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 5

4 Three-hinge arch Many 19 th century rail stations have three-hinge arches to avoid thermal stress and stress due to settlement. The hinges also facilitate transport. Hinges 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 6

5 Three-hinge arch Grimshaw s Waterloo Station, London, has three-hinge arches to avoid thermal stress and sttlement 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 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 7

6 Thermal strain 1 Bar of initial length L 2 Thermal strain ΔL due to heat, computed as: ΔL = αδtl where α = Coefficient of thermal expansion (in/in/ o F) Δt = temperature increase (+) / decrease (-) L = initial length 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 8

7 Coefficient of Thermal Expansion α and Elastic Modulus E Material US (10-6 in/in/ o F) E-Modulus US (10 6 psi) SI (10-6 m/m/ o C) E-Modulus SI (10 6 Pa) Aluminum Steel Concrete Masonry Wood Glass Plastics Thermal Thermal Stress Stress and and Strain, Strain Copyright G G Schierle, G press press Esc Esc to end, to end, for next, for next, for previous for previous slide slide 9

8 Thermal Stress 3. Bar of initial length L 4. Elongation ΔL due to heat 5. Hot bar reduced to initial length by load P 6. Thermal stress in restrained bar ΔL = αδt L ε = αδt E = f / ε f = ε E f = αδt E where f = thermal stress α = thermal coefficient Δt = temperature change E = elastic modulus 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 10

9 Curtain wall Assume: Aluminum curtain wall Fa = 10 ksi Δt = 100 o F (summer vs. winter temperature) 2 story mullion, L = 30 x 12 L = 360 α = 13 x 10-6 in/in/ o F E = 10 x 10 6 psi Expansion joint ΔL = αδt L ΔL = 13 x 10-6 x 100 o x 360 ΔL = 0.47 Use ½ expansion joint 0.5 > 0.47, ok Assume: Designer forgets expansion joint Thermal stress: f = αδt E f = 13x10-6 x100x10x10-6 = 13,000 psi f = 13,000 psi / 1000 Note: 10 6 and 10-6 cancel out and can be ignored f = 13 ksi 13 > 10, NOT ok 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 11

10 1 2 L Masonry expansion joint Space masonry expansion L = 100 Assume: Masonry Fa = 300 psi Temperature change Δt = 70 o F Joint spacing L=100 x 12 L = 1200 Thermal coefficient = 4x10-6 / o F E-modulus E = 1.5x10 6 psi Thermal expansion ΔL = Δt L ΔL = 4x10-6 / o Fx70 o x1200 ΔL = 0.34 Use 3/8 expansion joint > 0.34 Check thermal stress without expansion joint f = Δt E f = 4x10-6 x70 o x1.5x10 6 f = 420psi 420 > 300, NOT ok 3 4 Silicon joint 1 Building axon 2 Expansion joint in wall 3 Expansion joint at wall intersection 4 Expansion joint detail 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 12

11 Bridge expansion joints Bridges require expansion joints (roller or rocker) Assume Concrete bridge Span L = 310 x 12 L =3,720 Temperature change Δt = 90 o F Thermal coefficient = 6x10-6 / o F E-modulus E = 3x10 6 psi Thermal strain ΔL = Δt L ΔL = 6x10-6 x90 o x3720 ΔL = 2 Provide 2 ½ joint 2.5 > 2 Thermal stress without joint f = Δt E f = 6x10-6 x90 o x3x10 6 psi Too much stress without load f = 1,620 psi 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 13

12 Girder strain IIT 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 Δt = 107 o Thermal coefficient =6.5x10-6 / o F E-modulus E = 29x10 6 psi Girder strain ΔL = 6.5x10-6x107ox1440 ΔL = 1 Note: ½ girder elongation induces bending stress and deflection in columns 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 14

13 Please bring to next class engineering scale and 2 triangles 07 Thermal Stress and Strain Copyright G G Schierle, press Esc to end, for next, for previous slide 15