Me 202 - Iit Bombay

INDIAN INSTITUTE OF TECHNOLOGY, BOMBAY ME 202 – S1 - SOLID MECHANICS Tutorial Sheet # 2 Q1. The L-section shown in Figure (a) has second moments 𝐼! = 1, 512, 500 𝑚𝑚! , 𝐼! = 412, 500 𝑚𝑚! , 𝐼!" = − 450, 000 𝑚𝑚! about centroidal axes 𝑂!" . The centroid is located at the point (15,35) relative to the corner C as shown. The beam is subjected to a bending moment 𝑀 = 1000 𝑁𝑚 about the horizontal axis 𝑂! . Find the inclination of the neutral axis to 𝑂! and the location and magnitude of the maximum tensile stress in ! the section. Compare your results with the value 𝑀 !"# from the elementary bending ! !

theory.

Q2. A beam of circular cross section, radius 3𝑎 has two eccentric circular holes of radius a as shown in Figure (b). Find the centroid of the section and the second moments of area 𝐼! , _𝐼! , 𝐼!" about centroidal axes.

(a) Q3. Question to be given in the class.

(b)