Deflection of Beams · Strength of Materials Or Solid Mechanics · GATE CE
Marks 1
When a simply-supported elastic beam of span L and flexural rigidity EI (E is the modulus of elasticity and I is the moment of inertia of the section) is loaded with a uniformly distributed load w per unit length, the deflection at the mid-span is
$\rm \Delta_0=\frac{5}{384}\frac{wL^4}{El}$
If the load on one half of the span is now removed, the mid-span deflection _______.
Marks 2
For the 6m long horizontal cantilever beam PQR shown in the figure, Q is the midpoint. Segment PQ of the beam has flexural rigidity $EI = 2 \times 10^5$ kN. $m^2$ whereas the segment QR has infinite flexural rigidity. Segment QR is subjected to uniformly distributed, vertically downward load of 5 kN/m.
The magnitude of the vertical displacement (in mm) at point Q is _______ (rounded off to 3 decimal places).
The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams UV and WX are connected with the help of the vertical linear spring with spring constant k = 20 kN/m. The fixed supports are provided at U and X. It is given that flexural rigidity EI = 105 kN-m2, P = 100 kN, and a = 5 m. Force Q is applied at the center of beam WX such that the force in the spring VW becomes zero.
The magnitude of force Q (in kN) is __________. (round off to the nearest integer)

If the mid-span deflections of these beams are denoted by $${\delta _1}$$ and $${\delta _2}$$ (as indicated in the figures), the correct option is

If the flexural rrigidity $$(EI)$$ of the beam is $$30 \times {10^6}\,\,N$$ - $${m^2},$$ the maximum slope (expressed in radians) of the deformed beam is


The deflection of the beam at $$' R '$$ is

The deflection and slope of the beam at $$'Q'$$ are respectively


When the middle pontoon is removed, the deflection at $$H$$ will be

When the middle pontoon is brought back to its position as shown in the figure above, the reaction at $$H$$ will be
The bending moment at the middle support is
The reaction at the middle support is






Conjugate beam corresponding to this beam is



A load $$P$$ acts at mid-point of the rod $$BC$$. The downward deflection of joint $$B$$ is: