Calculate the maximum stress and bending curvature of a beam with the cross-section shown below and Young's Modulus E, subjected to a bending moment M. Assume no yielding. a=1, b=2, c=0.5, d=2 Example M H d a I b а

A wood beam with cross-sectional dimensions 200 mm x 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are E±= 190 GPa and Ew= 11 GPa, respectively. Also, the corresponding allowable stresses are eS= 110 MPa and ew = 7.5 MPa, (a) Calculate the maximum permissible bending moment Mmaxwhen the beam is bent about the- axis. Repeat part (a) if the beam is now bent about its y axis. Find the required thickness of the steel plates on the beam bent about the y axis so that Mmaxis the same for both beam orientations.

The cross section of a steel beam is shown in the figure. This beam is subjected to a bending moment M having its vector at an angle 8 to the - axis. Determine the orientation of the neutral axis and calculate the maximum tensile stress tiand maximum compressive stress tcin the beam. Assume that e = 22.5° and M = 4.5 kN · m. Use cross-sectional properties Ix=93.14 × 106 mm4, Iy= 152.7 X 10e mm4, and 9 = 27.3º.

A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure, (a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress (u in the copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.) (b) If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and ctqj = 700 MPa, what is the maximum bending moment Ml (c) What new value of copper diameter dtwill result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allow- able stress values at the same time).

A rectangular bar having width twice the depth is used as a beam. The beam is made of mild steel material having elastic modulus of 2.1 x 105 N/mm? and it undergoes bending by external load which makes radius of curvature of 150 m. If the allowable bending stress in the beam is to be limited to 100 MN/m. find the cross section of the beam.

The cross-sectional dimensions of a beam are shown. Assume b-2.125 in., tt-0.3125 in. and d=2.125 in. (a) If the bending stress at point K is 3360 psi (T), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress o, at point H (positive if tension, negative if compression). H N K Answers: bf (a) M₂ = i (b) σH = i d lb-ft. psi.

The simply supported beam with following cross section is loaded with concentrated loads and uniform load as shown. Determine a) the maximum tensile and compressive bending stress if P= 150 kip and w = 10 kip/ft, and b) the allowable uniform load w if the allowable bending stress is 24 Ksi and P = 15w. 3.169 in and c 1.5 inch Draw the FBD and calculate the reaction forces and shear and bending moment diagram. Draw the stress profile. Determine the maximum bending moment and its location 0.25 in. 3 ft 3 ft -0.25 in. 3 in. 10 ft 0.25 in. 3 in. -

y M B H B W Figure-2 A wide flange beam is subjected to a moment as shown in Figure-2. If M=10 kN.m, H=212 mm, W=170 mm, d=11 mm, t=18 mm and 0=64°; Btermine the momentOt lhadat about the axis- etermine the mement of inertia (mmabeut the avie y Betermine the normat stress (MPa due to bendng atpontA itic commressIive stress use Determine the orientation angle, B (degree), of the neutral axis relative to the +z axis.

The cross-sectional dimensions of a beam are shown. Assume b=3 in., tetw=0.4375 in. and d=3.375 in. (a) If the bending stress at point K is 1860 psi (T), determine the internal bending moment M, acting about the z centroidal axis of the beam. (b) Determine the bending stress oH at point H (positive if tension, negative if compression). K d H bf Answers: (a) M2 = i Ib-ft. ( b) σμ i psi. %3D Save for Later Attempts: 0 of 1 used Submit Answer

A beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: (i) The moment of inertia =  ii) The radius of curvature is  (iii) The maximum bending stress is in (N/mm^2) Answer and unit for part 3 iv) The bending stress at the point 0.6 cm from the neutral axis  is  in(N/mm^2) Answer and unit for part 4