Question

Question 1: A beam made of cast iron is fixed to a rigid wall on the left end. Yield strength of the cast iron is 270 MPa. At the right free end, an axial tensile force P is applied along the middle bottom of the beam, as shown in the following figure. Its cross section is an equilateral triangle with h=13 mm (note h #b for the triangle). The moment of inertia for the triangle is shown by the formula in the figure (N.A. stands for neutral axis). Point A is located at a distance of L = Im to the right end. For a static load P=0.173 KN, determine if point A is going to yield using Von Mises criteria. bh3 36 h23 N.A 1 = 48

Answer 1

ñ ar ky Given.. ( yield strength, Oy = 270 MPa h = 13 mm p = 0.173 KN (3) = 0.173 X1000 =173 N Solcetion: • The static load does not passes through cenboid of cross-section so this is eccentric problem. Here we will shift force p to New parallel position as shown in above figure, which result into an moment - M= P x h . M = 173* 3 .: M = 99.88 Namm 3

At 1 force ? boint A, we will have a stresses, Directi tensile stress due to an anial passing through centroid. Bending stress (compressive in nature to moment m. (2) due A - - - - - - - - - - - - - - - - - - - whol WB : Iya Ina = behind --- - N.A. в с In DABG = BC Jengo' = A .+ango' = BC = 1 mm - tangi . - 36 Base , b = 2x BC = 2 mm INA = bahan = 2X (3373 . INA = 288.68X103 mm4 tlenural eguation , Bending stress at A, By Jb INA M X y :: (T6), me n INA

y distance of point A from neutral anis. .. y = 2 = 2x13 = 1.155 mm . Conto = 99.88 X 1.155 288.68 x 10-3 . (a) = 399.62 MPa (compressive ) Axial tensile stress at A, Omd=Latex SA Good = 173 = 99.88 Mpa (T) IX 2X 53 2 102=0 fo-Corld 2D element stress at point A . . There is no .. Man, principal shear stress acts on the plane, stress, is 036-colch Ji - 399.62 - 99.88 r = 299.74 MPa (compressive) principal stress, on = 0 minimum

As stress es per von-mises criteria , working given by, ow = 10²+02-0,02 ris 299.74 MPa P =0 .: working stress ow = 0; = 299.74 Mpa material will yield only, If - ow > Tyield R ow > 270 MPa : point A is going to yield.