Which of the plot(s) shown is/are valid Mohrβs circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)
A beam of length πΏ is loaded in the π₯π¦ βplane by a uniformly distributed load, and by a concentrated tip load parallel to the π§ βaxis, as shown in the figure. The resulting bending moment distributions about the π¦ and the π§ axes are denoted by ππ¦ and ππ§ , respectively.
Which one of the options given depicts qualitatively CORRECT variations of ππ¦ and ππ§ along the length of the beam?
The figure shows a thin-walled open-top cylindrical vessel of radius π and wall thickness π‘. The vessel is held along the brim and contains a constant-density liquid to height β from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls.
Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress (Ο1) and circumferential wall stress (Ο2) on π¦?
Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Youngβs modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible.
The bars are held between rigid supports as shown in the figure and the temperature is raised by Ξπ. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by Ο1 and Ο2, respectively.
Which of the statement(s) given is/are CORRECT?
