List of top Structural Engineering Questions on Analysis of beams asked in GATE CE

The horizontal beam shown in the figure has fixed supports at F and L. Internal hinges are provided at locations G and J. The beam supports vertically downward concentrated loads as well as uniformly distributed loads, as shown in the figure.

(Figure not to scale)
Span F-G = 4 m carries a UDL of 5 kN/m. A 20 kN point load acts right at hinge G. A 30 kN point load acts at H, the midpoint of the hinge-to-hinge span G-J (G-H = H-J = 2 m each, hinge at J). Span J-K = K-L = 2 m each, with span K-L carrying a UDL of 4 kN/m.
The upward vertical reaction (in kN) at the support L is
A 3 m long, horizontal, rigid, uniform beam PQ has negligible mass. The beam is subjected to a 3 kN concentrated vertically downward force at 1 m from P, as shown in the figure. The beam is resting on vertical linear springs at the ends P and Q. For the spring at the end P, the spring constant Kp 100 kN/m.
beam is subjected to a 3 kN concentrated vertically downward
If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant KQ (in kN/m) for the spring at the end Q is
For a thin-walled section shown in the figure, points P, Q, and R are located on the major bending axis X - X of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange of the section.
For a thin-walled section
Qualitatively, the shear center of the section lies at
A linearly elastic beam of length 2l with flexural rigidity EI has negligible mass. A massless spring with a spring constant k and a rigid block of mass m are attached to the beam as shown in the figure.
linearly elastic beam of length 21
The natural frequency of this system is
For the 6 m long horizontal cantilever beam PQR shown in the figure, Q is the midpoint. Segment PQ of the beam has flexural rigidity EI = 2 × 105 kN.m2 whereas the segment QR has infinite flexural rigidity. Segment QR is subjected to uniformly, vertically downward load of 5 kN/m.
6 m long horizontal cantilever beam PQR
The magnitude of the vertical displacement (in mm) at point Q is ______ (rounded off to 3 decimal places).
The horizontal beam PQRS shown in the figure has a fixed support at point P, an internal hinge at point Q, and a pin support at point R. A concentrated vertically downward load (V) of 10 kN can act at any point over the entire length of the beam.
horizontal beam PQRS
The maximum magnitude of the moment reaction (in kN. m) that can act at the support P due to V is _______ (in integer).

Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity and is subjected to the external moments of magnitude \( M \) at one-third spans, as shown in the figure. Which of the following statements is/are TRUE? 

A propped cantilever beam EF is subjected to a unit moving load as shown in the figure. The sign convention for positive shear force at the left and right sides of any section is also shown. 
 

The CORRECT qualitative nature of the influence line diagram for shear force at G is