Topic outline

  • General

    This course covers general structural engineering.

    • Strain (ε), Stress (σ) and Radius of Curvature (R)



      A short tutorial to show you how to develop relationships between strain, stress, and radius of curvature.

      Strain (ε) = ΔL/L
      Modulus of elasticity (E) = stress/strain = σ/ ε
      E/R = σ/y

      Relationship between Bending Moment and Radius of Curvature: http://www.eurocoded.com/course/view.php?id=9#section-10

      • How to Derive Bending Equation aka Flexural Formula



        This video describes how to derive bending equation. This is also known as the flexural formula. Stresses resulted by bending moment are called bending or flexural stresses.

        Strain (ε), Stress (σ) and Radius of Curvature (R): http://www.eurocoded.com/course/view.php?id=9#section-9

        Pure bending: Stresses in an element caused by a bending moment applied to the element without axial, shear or torsion forces acting on the element.

        Theory behind the bending equation derivation has been developed for pure bending. Important points:
        • Plane sections remain plane after bending.
        • Beam material is homogenous and isotropic.
        • Beam is symmetrical about the plane of bending.
        • The stress-strain relationship is linear and elastic.
        • Young’s modulus remains the same for tension and compression.
        • Beam is initially straight and shape remains the same along the beam.

        I - Moment of inertia
        M - Bending moment
        σ - Bending stress
        y - Distance to the fibre from NA (Neutral axis)
        E - Modulus of elasticity
        R - Radius of curvature

        • Calculate Beam Deflections & Slopes Using Double Integration Method



          This video shows how you can calculate beam deflections using the double integration method.

          How to Derive Bending Equation aka Flexural Formula: http://www.eurocoded.com/course/view.php?id=9#section-10
          Strain (ε), Stress (σ) and Radius of Curvature (R): http://www.eurocoded.com/course/view.php?id=9#section-9

          R - Radius of curvature
          dy/dx - Slope
          M - Bending moment
          E - Modulus of elasticity
          I - Moment of inertia
          EI - Flexural stiffness

          Assumptions used to derive the differential equation of elastic curve:
          • Beam is stressed within the elastic limit i.e. stress is proportional to strain (Hooks law).
          • Beam curvature is very small.
          • Deflection resulting from the shear deformation of the material or shear stresses is neglected.
          • Simple bending theory (i.e. bending equation) is valid.

          Theory behind the bending equation derivation has been developed for pure bending. Important points:
          • Plane sections remain after bending.
          • Beam material is homogenous and isotropic.
          • Beam is symmetrical about the plane of bending.
          • The stress-strain relationship is linear and elastic.
          • Young’s modulus remains the same for tension and compression.
          • Beam is initially straight and shape remains the same along the beam.

          Pure bending: Stresses in an element caused by a bending moment applied to the element without axial, shear or torsion forces acting on the element.

          • Deflection & Slope - Cantilever Beam with a Point Load at the Free End



            This video shows how you can calculate deflection and slope of a cantilever beam with a point load at the free end using the double integration method.

            Differential Equation of the Elastic Curve: http://www.eurocoded.com/course/view.php?id=9#section-11
            Sign Convention: Bending Moment, Axial Force & Shear Force: http://www.eurocoded.com/course/view.php?id=9#section-4
            How to Derive Bending Equation aka Flexural Formula: http://www.eurocoded.com/course/view.php?id=9#section-10
            Strain (ε), Stress (σ) and Radius of Curvature (R): http://www.eurocoded.com/course/view.php?id=9#section-9

            M - Bending moment
            L - Length of the beam
            F - Force applied to the free end of the centilever beam
            dy/dx - Slope

            E - Modulus of elasticity
            I - Moment of inertia
            EI - Flexural stiffness

            Assumptions used to derive the differential equation of elastic curve:
            • Beam is stressed within the elastic limit i.e. stress is proportional to strain (Hooks law).
            • Beam curvature is very small
            • Deflection resulting from the shear deformation of the material or shear stresses is neglected.
            • Simple bending theory (i.e. bending equation) is valid

            Theory behind the bending equation derivation has been developed for pure bending. Important points:
            • Plane sections remain after bending.
            • Beam material is homogenous and isotropic.
            • Beam is symmetrical about the plane of bending.
            • The stress-strain relationship is linear and elastic.
            • Young’s modulus remains the same for tension and compression.
            • Beam is initially straight and shape remains the same along the beam.

            Pure bending: Stresses in an element caused by a bending moment applied to the element without axial, shear or torsion forces acting on the element.

            • How to Calculate Support Reactions of a Cantilever Beam with a Point Load



              A short tutorial showing how to calculate reactions at the support of a simple cantilever beam with a point load applied on to it. We look at vertical equilibrium and moment equilibrium to determine the reactions at the fixed end of the beam. You can use this as the starting point to draw bending moment diagram and shear force diagram of a cantilever beam with a point load applied on to it.

              • How to Calculate Support Reactions of a Cantilever Beam with a Uniformly Distributed Load



                A short tutorial with a numerical worked example to show how to determine the reactions at the support of a cantilver beam with uniformaly distributed load only applied to a part of the beam.

                Related videos:

                How to Calculate Support Reactions of a Cantilever Beam with a Point Load: http://www.eurocoded.com/course/view.php?id=9#section-5
                Deflection & Slope - Cantilever Beam with a Point Load at the Free End: http://www.eurocoded.com/course/view.php?id=9#section-4
                How to Calculate Support Reactions of a Simply Supported Beam with a Point Load: http://www.eurocoded.com/course/view.php?id=9#section-6

                • How to Calculate Support Reactions of a Simply Supported Beam with a Point Load

                  • How to Draw a Free Body Diagram - Simply Supported Beam with a Point Load



                    A short video to show you how to form an imaginary cut and draw a free body diagram of a simply supported beam with a point load.

                    • How to Calculate Support Reactions of a Simply Supported Beam with a Uniformly Distributed Load (UDL)



                      A short tutorial with a numerical worked example to show how to determine the reactions at supports of a simply supported beam with a uniformly distributed load (also known as UDL).

                      • How to Resolve Forces or Split a Force in to Two Components and Combine Forces



                        A video tutorial to show you how to resolve a force into two components. Two components considered in this video are the rectangular components (one in X direction or horizontal direction and one in Y direction or vertical direction). I have included a numerical example to get a better understanding.

                        Conversely we look at how to combine the two rectangular forces into a single force. This is called composition of forces.

                        • Sagging Bending Moment and Hogging Bending Moment



                          A short video explaining sagging bending moments and hogging bending moments using
                          1. A simply supported beam with a point load in the middle
                          2. A fixed end cantilever beam with a point load at the free end

                          Watch the video to get a clear idea about the tensile and compressive stresses due bending moments along with the deflected shapes where sagging and hogging bending moments occur.

                          Sign Convention - Bending Moment, Axial Force & Shear Force: http://www.eurocoded.com/course/view.php?id=9#section-4
                          Tension and Compression in Structural Sections (Beam & Column): http://www.eurocoded.com/course/view.php?id=9#section-3

                          • Tension and Compression in Structural Sections (Beam & Column)

                            • Sign Convention: Bending moment, Axial force, Shear force & Torque



                              When analysing structural member they are cut into sections and typical sign convention is

                              • Sagging bending moment is positive
                              • Hogging bending moment is negative
                              • Tensile axial force is positive
                              • Compressive axial force is negative
                              • Clockwise rotation (direction) shear force couples are positive
                              • Anti-clockwise direction torque is positive

                              • Section Modulus - Definition, Example, Use and Units



                                Section Moduli - Plastic Section Modulus (Wpl) & Elastic Section Modulus (Wel)

                                • Method of Joints Example Calculation - Truss Analysis - External and Internal Forces on a Truss




                                  The method of joints is a process you can use to determine internal forces in a truss structure. The principle behind method of joints is the equilibrium. In another words all forces acting on a joint must add up to zero. If the forces acting on a joint don’t add up to zero then the joint would not be in equilibrium; meaning the joint would move. In this example we show you how to calculate external forces on a truss structure and then how to calculate internal force in the members of the truss.

                                  Structural Support Types and Restraints They Offer: http://www.eurocoded.com/course/view.php?id=9#section-11

                                  • Structural Support Types and Restraints They Offer

                                    • Concrete Class/Grade - Concrete Compressive Strength Class



                                      The minimum characteristic cylinder strength is determine by compression tests on 150mm diameter by 300mm length concrete cylinders and the minimum characteristic cube strength is determine by compression tests on 150mm edge length concrete cubes.

                                      C - Normal-weight or heavy-weight concrete compressive strength classes
                                      LC - Light-weight concrete compressive strength classes

                                      Codes/Standards:
                                      • EN 199 2 - Design of concrete structures
                                      • EN 206 - Concrete - Specification, performance, production and conformity

                                      • What is Reinforced Concrete? What is Compatibility of Strains?

                                        • Mathematics Formulae

                                          Trigonometrical Formulae



                                          • Glossary