Keller's *Keller Webinar Series: Liquefaction Mitigation* begins at __27 Oct 2021__

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

Contents [show]

**The rod of the picture is loaded with the force 2P which is uniformly distributed on Section D where applied. If the material of the rod is homogenous with Elastic Modulus E find the variation in length of the rod. The area of the cross section in part AC is 2A while CD is A.**

__Solution__

We calculate the reaction R at the rigid end connection A from the equilibrium of forces.

ΣP_{X}= 0 → 2P - R = 0 → R = 2P **(1)**

The rod doesn’t have everywhere constant area of cross section so we examine parts AC and CD.

At part AC the cross section with area 2A is loaded with axial force equal to R. So at this part we have equal uniform stress σ_{1} and deformation ε_{1}.

σ_{1} = R / 2A

ε_{1} = Δl_{1} / L

Because stress is equal and the material is homogenous Hook Law is applied for section AC.

σ_{1}= Eε_{1 }→ R / 2A = E ( Δl_{1 }/ L) →Δl_{1 }= (R / 2A) (L / E) **(2)**

At part CD we have axial force 2P so:

σ_{2} = 2P / A

ε_{2} = Δl_{2} / 3L

And Hooks Law:

σ_{2} = Eε_{2 }→ 2P / A = E (Δl_{2} / 3L) → Δl_{2}= (2P / A )(3L / E) **(3)**

From equations (1),(2),(3) we have the total change of length of the rod.

Δl= Δl_{1} + Δl_{2} = (R / 2A)(L / E) + (2P / A)(3L / E)

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 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 ExamplesSpring Assemblies in Series/Parallel: Two Springs in SeriesTruss vs CableCalculate the vertical deflection of a beamFlexular Crack in Concrete BeamMaximum Factored Vertical Shear

A simply supported beam (Figure) with a span...

For the simply supported beam of Figure 1, deter...

Calculate the vertical deflection of the beam (m...

Truss and cable elements are defined by their ab...

Based on Figure 1, we get: where:...

_