Stress condition for point M will be as shown in the figure.
As, $ \style{font-family:'Times New Roman'}{{\mathrm\tau}_\mathrm{xy}} $ represents the shear at free surface so it will be zero.
$ \mathrm\delta=5\;\mathrm{mm}=\frac{\mathrm p\mathcal l^3}{3\mathrm{EI}} $
Max. bending stress at free and $ =\frac{{\mathrm{MY}}_\max}{\mathrm l} $
$ \begin{array}{l}{\mathrm f}_\max=\frac{\mathrm P\mathcal l{\mathrm y}_\max}{\mathrm i}\\\frac{{\mathrm f}_\max}{\mathrm\delta}=\frac{\mathrm P\mathcal l{\mathrm y}_\max}{\mathrm l\times{\displaystyle\frac{\mathrm p\mathcal l3\mathcal l^2}{3\mathrm{El}}}}=\frac{{\mathrm y}_\max\times3\mathrm E}{\mathcal l^2}\\{\mathrm f}_\max=\mathrm\delta\left[\frac{{\mathrm y}_\max\times3\mathrm E}{\mathcal l^2}\right]\\\;\;\;\;\;\;=\frac{5\times10^{-3}\mathrm m\times{\displaystyle\frac{0.1}2}\mathrm m\times3\times2\times10^{11}\mathrm N/\mathrm m^2}{(2)^2\mathrm m^2}\\\;\;\;\;\;\;=\frac{5\times0.6}8\times10^8\mathrm N/\mathrm m^2\\\;\;\;\;\;\;=\frac{5\times60}8\mathrm{MPa}=\frac{300}8\mathrm{MPa}=37.5\;\mathrm{MPa}\end{array} $
For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.
The shear stress $ \style{font-family:'Times New Roman'}\tau $ is
A haunched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity 10 kN/m. The design shear force (expressed in kN) at the section X-X of the beam is ______
A 450 mm long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as 150 mm × 150 mm. Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in MPa) is ________
Two beams are connected by a linear spring as shown in the following figure. For a load P as shown in the figure, the percentage of the applied load P carried by the spring is ________.
A symmetric I-section (with width of each flange 50 mm,thickness of each flange = 10 mm,depth of web = 100 mm, and thickness of web =10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress(in N/mm^{2} the web at its junction with the top flange. __________