Q1: Residual Stress in Plastically Deformed Beam M M 2h +c. A slender 2D beam with a solid rectangular cross section of dimensions b-40mm and 2h=80mm is designed to exhibit linear elastic behaviour under operating bending moment M = 9.5 kNm. ii. 9 Assume a bilinear hardening material model with material properties dy = 300 MPa, E = 200E3 MPa and ET = 20E3 MPa. a) M = 6 Calculate the stress at the top and bottom surfaces of the beam when M = 9.5 kNm, and hence determine the reserve factor against yield during normal operation. Er h³1 3 Ec b) During installation, the beam is subject to an accidental-overload moment of M = 14kNm, causing limited plastic deformation. You may assume the bilinear hardening beam equilibrium equation without derivation: ET = 2boy [(1 - 4/7) (1/2² - 6) + where tc is the boundary between the elastic core and the plastic zones. [2 marks] i. Calculate the stress at the top and bottom surfaces of the beam at maximum load M = 14 kNm. See the Note below for suggestions on how to solve the equilibrium equation for c. [9 Marks] Calculate the residual stress at the top and bottom surfaces of the beam after unloading to M = 0 and sketch the residual stress distribution through the depth of the beam.

Fig: 1