Verification Examples

Using AISC Manual tables, determine the available compressive and flexural strengths and if the ASTM A992 W14x99 beam has sufficient available strength to support the axial forces and moments shown in Figure 1, obtained from a second-order analysis that includes P-𝛿 effects.

Determine the required strengths and effective length factors for the ASTM A992 material columns in the moment frame shown in Figure 1 for the maximum gravity load combination, using LRFD and ASD.

A single-mass system with dashpot is subjected to a constant loading force. Determine the spring force, the damping force and the inertial force at given test time. In this verification example, the Kelvin--Voigt dashpot, namely, a spring and a damper element in serial connection, is decomposed into its purely viscous and purely elastic parts, in order to better evaluate the reaction forces.

A very stiff cable is suspended between two supports. Determine the equilibrium shape of the cable, the so-called catenary, consider the gravitational acceleration and neglect the stiffness of the cable. Verify the position of the cable at given test points.

A column is composed of a concrete part - rectangle 100/200 and of a steel part - profile I 200. It is subjected to pressure force. Determine the critical load and corresponding load factor. The theoretical solution is based on the buckling of a simple beam. In this case two regions have to be taken into account due to different moment of inertia and material properties.

Thin rectangular orthotropic plate is simply supported and loaded by the uniformly distributed pressure. The directions of axis x and y coincide with the principal directions. While neglecting self-weight, determine the maximum deflection of the plate.

A thin circular ring of rectangular cross-section is exposed to an external pressure. Determine the critical load and corresponding load factor for in-plane buckling.

A single mass system with dashpot is subjected to the constant loading force. Determine the deflection and the velocity of the dashpot endpoint in given test time.

A quarter-circle beam with a rectangular cross-section is loaded by means of an out-of-plane force. This force causes a bending moment, torsional moment and a transverse force. While neglecting self-weight, determine the total deflection of the curved beam.

A curved beam consists of two beams with a rectangular cross-section. The horizontal beam is loaded by a distributed loading. While neglecting self-weight, determine the maximal stress on the top surface of the horizontal beam.

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