Create a free account and view content that fits your specific interests in structural engineering Learn More
Contents [show]
Determine the equation of the elastic curve for the beam using the x coordinate. Specify maximum deflection. EI is constant.
Solution
Free body diagram:
Elastic curve:
Also u=0 at x=0.
Slope: Substitute the value of C1 into (1)
Elastic Curve: Substitute the value of C1 and C2 into (2)
Deflection max at x=L/2
Selected Topics
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 – Member Diagram.Calculation Example – Minimum allowable Diameter.Calculation Example – Critical load.Calculation Example – Simple harmonic vibration part1Calculation 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
Want to read more like this?
Calculation Example - Calculate the equation of the elastic curve.
Jan, 25, 2017 | EducationCalculate the equation of the elastic curve .Determine the pinned beam’s maximum deflection. EI cons...
Calculation Example – Frame analysis.
Apr, 13, 2016 | EducationCalculate the reactions and member forces. Solution We calculate the reactions. Section 1 0...
Calculation Example – Frame analysis – Uniform Load
May, 09, 2016 | EducationCalculate the reactions and member forces. Solution We calculate the reactions. ...
Beams: maximum moment
Jun, 07, 2022 | EducationFind the maximum moment of the above beam which is subjected to triangular vertical load. SOLUTION:...
Calculation of the cross-sectional area and the position of centroid
Apr, 04, 2024 | EducationThe problem: Determine the cross-sectional area and the position of the centroid for the sectio...
Calculation of the second moments of area
Apr, 12, 2024 | EducationThe problem: Determine the second moments of area, Ixx and Iyy, for the sections indicated in...
Calculate the location of point load
Feb, 14, 2019 | EducationCalculate the distance x for locating point load so that the moment on the beam at point B is zero....
Calculation Example – Beam with inner hinge (Part B). Calculate the member diagrams.
Mar, 17, 2016 | EducationCalculate the member diagrams. Solution We have already calculated the external beam rea...
Truss deflection using the unit load method
Aug, 28, 2023 | EducationGiven: A pin-jointed truss is given in Figure 1. Determine the vertical displacement of join...
Trending
Jun, 18, 2019 | Education
Calculate the Maximum Shear Stress
Sep, 16, 2022 | Education
Diaphragms
Aug, 05, 2019 | Education
How to calculate yield strength
Sep, 16, 2022 | Education
Structural stability
Mar, 01, 2024 | Education
Overhanging beam: shear force and bending moment calculation
Oct, 04, 2017 | Education
Calculation Example – Plastic Neutral Axis.
Sep, 08, 2015 | Education
Calculation Example: Axial Force On A Column
Jun, 29, 2023 | Education