For a loaded cantilever beam of uniform cross-section, the bending moment (in N mm) along the length is M(x)=5x^{2}+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm is__________
The Figure shows cross-section of a beam subjected to bending. The area moment of inertia $(\mathrm{in}\;\mathrm{mm}^4)$ of this cross-section about its base is _________ .
A simply supported beam of length 2L is subjected to a moment M at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 ≤ x ≤ L$ is given by
$w=\frac{-Mx}{12\;EIL}\left(L-x\right)\left(x+c\right)$ ,
where E is the Young’s modulus, I is the area moment of inertia and c is a constant (to be determined) .
The slope at the center $x = 0$ is
A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of 10 kN is applied at the midpoint of PQ. The magnitude of bending movement (in kN-m) at fixed end O is
For the overhanging beam shown in figure, the magnitude of maximum bending moment (in kN-m) is _____.
A simply supported beam of length L is subjected to a varying distributed load sin (3$\pi $ x/L) Nm^{-1}, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is
A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-span of the beam as shown in the figure. The reaction forces R_{P} and R_{Q} at supports P and Q respectively are
A massless beam has a loading pattern as shown in the figure. The beam is of rectangular cross-section with a width of 30mm and height of 100mm.
The maximum bending moment occurs at
The maximum magnitude of bending stress (in MPa) is given by
In a simply – supported beam loaded as shown below, the maximum bending moment in Nm is
A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are
A machine frame shown in the figure below is subjected to a horizontal force of 600 N parallel to z – direction.
The normal and shear stresses in MPa at point P are respectively
The maximum principal stress in MPa and the orientation of the corresponding principal plane in degrees are respectively