The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure. Several types of coefficients have been developed: volumetric, area, and linear. Which is used depends on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, or over some area. The volumetric thermal expansion coefficient is the most basic thermal expansion coefficient. In general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions. Substances that expand at the same rate in every direction are called isotropic. For isotropic materials, the area and linear coefficients may be calculated from the volumetric coefficient. For an isotropic I beam the linear expansion coefficient is and the volumetric expansion coefficient is equal to 3 ALPHA . Part A An I beam is at 40 C and clamped rigidly between two fixed points, 2 meters apart, so that it can neither expand nor contract. The breaking stress of the beam is 230 MPa and the coefficient of linear expansion ( ) is 1.8 x 10-5 /oC and Young's Mod = 115 GPa. If the beam were free to expand, without restrictions, what would the length of the beam be at 140 oC? Length (cm) = cm Part B An I beam is at 40 C and clamped rigidly between two fixed points, 2 meters apart, so that it can neither expand nor contract. The breaking stress of the beam is 230 MPa and the coefficient of linear expansion ( ) is 1.8 x 10-5 / oC and Young's Mod = 115 GPa. What is the force exerted on the wall if the beam has a cross-sectional area of 58 cm2? Compressive Force = Newtons Part C An I beam is at 40 C and clamped rigidly between two fixed points, 2 meters apart, so that it can neither expand nor contract. The breaking stress of the beam is 230 MPa and the coefficient of linear expansion ( ) is 1.8 x 10-5/oC and Young's Mod = 115 GPa. As the beam warms, at what temperature would the bar rupture? Rupture temperature = 0C