THERMAL STRESS ENGR. ROGELIO FRETTEN C. DELA CRUZ, CE INSTRUCTOR
THERMAL STRESS
It is the stress resulting from thermal expansion (or contraction) of a body when subjected to thermal changes. The expansion (or contraction) of a body undergoing thermal deformation is given by:
Procedure for deriving compatibility equations: •
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Remove all applied loads and constraints so that thermal deformation can freely occur. Sketch the thermal deformation using exaggerated scale. Apply the forces that are necessary to restore the specified conditions of restraint. Obtain geometric relations between the temperature and load deformation from the sketch of the problem. Apply conditions of equilibrium.
Problem 1. A steel rod 2.5 m long is secured between two walls. The cross-sectional area of the rod is 1200 mm 2, α = 11.7 μm/(m·°C), and E = 200 GPa. The load on the rod is zero at 20°C. Compute the stress when temperature drops to – 20°C, assuming that (a) the walls are rigid, and (b) the walls spring together a total distance of 0.50 mm as the temperature drops.
Problem 2. The bronze bar 3 m long with a cross-sectional area of 350 mm2 is placed between two rigid walls. At a temperature of – 20 °C, there is a gap Δ = 2.2 mm, as shown in the figure. Find the temperature at which the compressive stress in the bar will be 30 MPa. Use α = 18 × 10-6 /°C and E = 80 GPa.
Problem 3. A steel rod is stretched between two walls. At 20 °C, the tensile force in the rod is 5000 N. If the stress is not to exceed 130 MPa at – 20°C, find the minimum allowable diameter of the rod. Use α = 11.7 × 10-6/°C and E = 200 Gpa.
Problem 4. A steel rod with cross-sectional area of 0.25 in 2 is stretched between two fixed points. The tensile force in the rod at 70°F is 1200 lb. α = 6.5 × 10-6/°F and E = 29 × 106 psi. a) What will be the stress at 0°F? b) At what temperature will the stress be zero?
Figure shows a homogeneous, rigid block weighing 12 kips that is supported by three symmetrically placed rods. The lower ends of the rods were at the same level before the block was attached. Determine the stress in each rod after the block is attached and the temperature of all bars increases by 100 °F, given the following data:
The compound bar, composed of the three segments shown, is initially stress-free. Assuming the walls do not yield, compute the stress in each material if the temperature drops 25°C, given the following data: A
