Question

The material is structural steel with of = 220 MPa, E = 200 GPa, v = 0.3, and a = 12x10-6 / 0 C The steel rod (Figure 1) is constrained between two rigid surfaces. It has a diameter D = 20 mm and is subjected to load P = 20 kN. Consider the following value below The reaction at 'A' = 13.13 KN(t) The reaction at 'B' = 6.67 KN(t) The stress in section AC = 42.4 Mpa (T) The change in length of section BC = -0.0848mm The change in diameter in section AC = -1.27x10^-3 mm If the rod's temperature was to change by AT = 1000 C Calculate 1. The maximum compressive stress due to both P and temperature change. 2. The maximum shear stress 3. The factor of safety (if any) according to Tresca's criteria

Please provide a correct answer to these questions.

Answer 1

Solution RA A Considering only load 'p' RA= 13.33 kN. Rp = 6.62 kN . с Stress in AC, AC = 42-44MPa. (tensile), B- Stress in BC, Sac (RA-P) RB. Que to lood's only Area =1133–20 )x103 =~21.23 MPa (compressive) Now if nod temperature is increased by 100°c. thermal stress in rod doTE = (12x10 x 108* (2004) 240 MPa (Compressive) Cumonelative effect of 'p' and AT. compressire, GAC 42.4 -240= - 197.6 et MPa ( Goca - 21-23 - 240=-26 1.23 MPa. (Compressive) mare Compressive stress = 261.23 MPa and it is in Bc

moremum shear stress. АС Emore = arba), Erse one principal stress 6,2= betby & -by + kg hore only onial stress is acting 6 = 6AC = 287. - 192.6 MPa 6220 :. | Trolne = 1-1926.- =98.8 MPa Вс Similarly. Emore 1-261.23-01 = 130.61 MPa maximum shear stress) = 13061 MPa. Bc. (3) Factor of safety AC Bc. Emen s j 2 N Tman Sg > 8-9 is 220 » 13061 S 220 > N S lill N=0.84 No 1.11 i For sale design factor of solety should be loll.