Stresses in Machine Elements Lecture Number - 03 Venkat S Mechanical Engineering SINHGAD COLLEGE OF ENGG,vadgaon Strength of Materials

C-Section 1.Fig-1 shows the section of an inverted steel channel used as a beam.The beam is simply supported over a span of 3 meters and carries two equal concentrated loads at points distant 0.30 m from each support. Find the value of each of these loads if the maximum tensile stress is not to exceed 95 N/mm 2.Find also the corresponding maximum compressive stress. Strength of Materials

Solution Let each point load be W Newton Each vertical reaction = W Newton Max B.M =M=Wx300Nmm. Distance of the neutral axis from the top edge = Strength of Materials

Continuation Distance of the neutral axis from the bottom edge = =72.33mm When the maximum tensile stress is 95 N/mm 2 corresponding maximum compressive stress Strength of Materials

Continuation Moment of inertia about the neutral axis Strength of Materials

Continuation Strength of Materials

Example-1 A beam ABC 6m long is supported at A and B 4m apart with an overhang of 2m. The beam carries a uniformly distributed load of 3 kN/m over the whole length. The proposed section for the beam is shown in fig-4.Determine the extreme stresses produced in the beam. Strength of Materials

Solution Steps Solution syntax: Taking moments about the left end A, Strength of Materials Then find out: Maximum sagging bending moment (M d )=3.375 kNm Maximum negative bending moment (M b )=-6 kNm

Continuation Properties of the section : Distance of the centroidal axis from the top edge Strength of Materials Find out : Distance of the centroidal axis from the bottom edge ? Moment of inertia of the section about the centroidal axis I ? Maximum stresses due to maximum sagging moment : compressive stress at top edge ? Tensile stress at bottom edge ?

Continuation Maximum stresses due to maximum hogging moment: Tensile stress at the top edge ? Compressive stress at the bottom edge ? Strength of Materials

Example-2 A steel channel section, ISLC 225 is used as a simply supported beam on a span of 4m. The channel is to be designed for a working bending stress of 100 N/mm 2. It has to carry a uniformly distributed load on the whole span. Calculate the permissible load when (i) the channel stands upright 225 mm high (ii) the channel lies flat with the 225 mm horizontal The properties of the channel ISLC 225 are, A=3053 mm 2 I xx =2547.9x10 4 mm 4, I yy = x 10 4 mm 4, C yy =24.6 mm Depth=225mm, Flange width= 90 mm Strength of Materials

Solution Steps (i)When the channel is placed with the 225 mm dimension vertical Maximum B.M that can be resisted Let the safe load on the beam be w N/m w=11324 N/m Strength of Materials

Continuation (ii)When the channel is placed with the 225 dimension horizontal In this case,maximum B.M that can be resisted Strength of Materials

Continuation Let the safe load on the beam be w N/m. Strength of Materials