Centroid and Moment of Inertia · Strength of Materials Or Solid Mechanics · GATE CE

Marks 1

The steel angle section shown in the figure has elastic section modulus of 150.92 cm³ about the horizontal X−X axis, which passes through the centroid of the section.

The shape factor of the section is ______ (rounded off to 2 decimal places).

GATE CE 2024 Set 2

Polar moment of inertia $$\left( {{{\rm I}_p}} \right),$$ in $$c{m^4},$$ of a rectangular section having width, $$b=2$$ $$cm$$ and depth $$d=6$$ $$cm$$ is __________

GATE CE 2014 Set 2

The first moment of area about the axis of bending for a beam cross-section is

GATE CE 2014 Set 2

Marks 2

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.

The natural frequency of this system is

GATE CE 2024 Set 2

Consider the horizontal axis passing through the centroid of the steel beam cross-section shown in the figure. What is the shape factor (rounded off to one decimal place) for the cross-section?

GATE CE 2023 Set 1

The cross-section of a girder is shown in the figure (not to scale). The section is symmetric about a vertical axis (Y - Y). The moment of inertia of the section about the horizontal axis (X - X) passing through the centroid is _______ cm4 (round off to nearest integer).

GATE CE 2023 Set 1

A disc of radius $$'r'$$ has a hole of radius $$'r/2'$$ cut-out as shown. The centroid of the remaining disc (shaded portion) at a radial distance from the center $$''O''$$ is

GATE CE 2011

For the section shown below, second moment of the area about an axis $$d/4$$ distance above the bottom of the area is

GATE CE 2006