Create a free account and view content that fits your specific interests in structural engineering __Learn More__

Contents [show]

A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation

where ω is a positive constant.

a) Show that

and

are equivalent.

**Solution**

So the form is x(t)=A sinωt+B cosωt

where

x(t)=A sinωt+B cosωt

with

Calculation Example: Natural Periods of Vibration for SystemsCalculation Example: Axial Force On A ColumnCalculation Example: Shear force On A ColumnCalculation Example: Overturning Moment for Shear panelCalculation Example: Calculate the Change in Length of a Rod loaded in extensionCalculation Example - Calculate the Axial Forces on the Truss MembersCalculation Example - Calculate the member diagramsCalculation Example - Calculate the member diagrams for the beamCalculation Example – Beam with inner hinge (Part A). Find the ReactionsCalculation Example – Beam with inner hinge (Part B). Calculate the member diagrams.Calculation Example – Frame analysis.Calculation Example – Frame analysis – Uniform LoadCalculation Example – Find the Center of Gravity (Surface)Calculation Example – Design bolted connection of tension plates (EC3)Calculation Example – Cantilever BeamCalculation Example – Cantilever Beam, Temperature changeCalculation Example – Undamped free Vibration (Part A).Calculation Example – Undamped free Vibration (Part B).Calculation Example – Evaluation of Structural Property Matrices.Calculation Example – Angular acceleration, angular velocity.Calculation Example – Shear bolt connection EC3.Calculation Example – Buckling of Column (EC3).Calculation Example - Calculate the member diagrams.Calculation Example - Calculate the member diagrams.Calculation Example - Calculate the equation of the elastic curve.Calculation Example - Calculate the location of support.Calculation Example – Plane stress.Calculation Example - Annular cross section, Stress.Calculation Example – Allowable shear force for the girder.Calculation Example - Calculate the deflection. Castigliano Theorem.Calculation Example – Determine the shear force and moment.Calculation Example – Determine the magnitudes of F1,F2.Calculation Example – Internal forces.Calculation Example - Calculate the Axial Forces of the Truss Members.Calculation Example – Calculate the moments of inertia Ix and Iy.Calculation Example – Calculate shear stress for temperature load.Calculation Example – Calculate tension force using virtual work.Calculation Example – Torsional moment-Stress.Calculation Example – Reinforced Concrete Column at Stress.Calculation Example – Cantilever Beam with uniform loading.Calculation Example – Cantilever Beam with point loads.Calculation Example – Rod loadingCalculation Example – Maximum DeflectionCalculation Example – Member Diagram.Calculation Example – Minimum allowable Diameter.Calculation Example – Critical load.Calculation Example – Simple harmonic vibration part 2Calculation Example – FrictionCalculation Example – Section Modulus SCalculation Example – Plastic Neutral Axis.Calculation Example – Buckling of Column (EC3).Calculation Example – Shear bolt connection EC3.Calculation Example – Member Diagram. Triangular load.Calculation Example – Torsional moment-Stress.Calculation Example – Angular acceleration, angular velocity.Calculate the location of point loadShear bolt connection EC3Torsional Moment-StressCalculate the Axial Forces of the Truss MembersCalculate the Maximum Shear StressHow to calculate yield strengthCalculate angular velocity, angular accelerationTemperature ChangeAverage shear stress in pressure vesselAllowable shear force of the girderCalculation ExamplesCalculate the variation in length of the rodSpring Assemblies in Series/Parallel: Two Springs in SeriesTruss vs CableCalculate the vertical deflection of a beamFlexular Crack in Concrete BeamMaximum Factored Vertical ShearColumn in bucklingBeams: maximum momentNominal flexural strength of a reinforced concrete beamCalculation of the cross-sectional area and the position of centroidCalculation of the second moments of areaExample: longitudinal reinforcement for shear and torsion according to EC2

A single point with mass m is vibrating harmonically. The displacement x from point of balance is go...

The problem: Determine the cross-sectional area and the position of the centroid for the sectio...

The problem: Determine the second moments of area, Ixx and Iyy, for the sections indicated in...

Calculate the distance x for locating roller support so that the moment on the beam at point B is ze...

Calculate the equation of the elastic curve .Determine the pinned beam’s maximum deflection. EI cons...

Calculate the reactions and member forces. Solution We calculate the reactions. Section 1 0...

Calculate the reactions and member forces. Solution We calculate the reactions. ...

Calculate the member diagrams. Solution We have already calculated the external beam rea...

Find the maximum moment of the above beam which is subjected to triangular vertical load. SOLUTION:...

Jun, 18, 2019 | Education #### Calculate the Maximum Shear Stress

Sep, 16, 2022 | Education #### Diaphragms

Aug, 05, 2019 | Education #### How to calculate yield strength

Aug, 28, 2023 | Education #### Truss deflection using the unit load method

Sep, 16, 2022 | Education #### Structural stability

Jun, 29, 2023 | Education #### Nominal flexural strength of a reinforced concrete beam

Sep, 08, 2015 | Education #### Calculation Example: Axial Force On A Column

Mar, 01, 2024 | Education #### Overhanging beam: shear force and bending moment calculation

Sep, 25, 2024 | Education #### Example: longitudinal reinforcement for shear and torsion according to EC2