In this video we'll take a detailed look at trusses. Trusses are structures made of up slender members, connected at joints which can be approximated to pinned connections.

It is typically assumed that loads are applied to the joints of the truss, not directly to the members. Because of this, the members only carry axial forces - they do not carry bending moments. The internal force in each member is constant, and a member can be either in tension or in compression.

It is important for engineers to be able to determine the axial force in the members of a truss, so that they can be designed appropriately. In this video I cover the two main methods for doing this, which are the Method of Joints and the Method of Sections.

The Method of Joints involves applying the equilibrium equations to solve the internal forces acting on every joint within the truss.

The Method of Sections involves creating an imaginary cut through the members of interest, and applying the equilibrium equations to the external and internal forces

In this video we take a look at five methods that can be used to predict how a beam will deform when loads are applied to it. These are the double integration method, Macaulay's method, the principle of superposition, the moment-area method, and Castigliano's theorem, which is based on strain energy.

00:00 - Introduction

01:58 - Double Integration Method

08:19 - Macaulay's Method

12:07 - Superposition Method

13:20 - Moment-Area Method

17:24 - Castigliano's Theorem

20:26 - Outro

In this video we explore bending and shear stresses in beams. A bending moment is the resultant of bending stresses, which are normal stresses acting parallel to the beam cross-section. We can easily derive an equation for these bending stresses by observing how a beam deforms for a case of pure bending. This equation is know as the flexure formula.

Next we look at shear stresses, which act parallel to the beam cross-section, and can be represented by a shear force. These vertical shear stresses can cause horizontal shear failure in beams, because they result in complementary horizontal shear stresses, which develop to maintain equilibrium.

Finally we look at how we can apply the shear stress equation to thin-walled open sections like the I beam, and how shear stress appears to "flow" through the cross-section.

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ERRATA:

- The moment shown at 07:38 is drawn in the wrong direction.

- The shear stress profile shown at 11:41 is incorrect - the correct profile has the maximum shear stress at the edges of the cross-section, and the minimum shear stress at the centre.

Did you know that the typical stress-strain curve obtained from a uniaxial tensile test is just an approximation? It doesn't consider the fact that the dimensions of the test specimen change throughout the duration of the tensile test.

In this video I cover the interesting topic of true stress and true strain.

This video is an introduction to stress and strain, which are fundamental concepts that are used to describe how an object responds to externally applied loads.

Stress is a measure of the distribution of internal forces that develop within a body to resist these applied loads.

There are two main types of stress - normal stress, which acts perpendicular to a surface, and shear stress, which acts parallel to a surface.

Strain is a measure of the displacements that occurs within a body. Again we have both normal and shear stresses. 

In this video I also discuss stress-strain curves, which define how stress and strain are related. Different materials have different stress-strain curves, which can be determined by performing a tensile test.

The stress state at a single point within a body is actually made up components in both the normal and the shear directions. I explore this idea at the end of the video but looking at stresses obtained when we cut a bar using an inclined plane.

Young's modulus is a crucial mechanical property in engineering, as it defines the stiffness of a material and tells us how much it will deform for an applied stress.

In this video I take a detailed look at Young's modulus, starting with tensile tests and stress-strain curves, all the way through to what is happening at the atomic scale.

Strength, ductility and toughness are three very important, closely related material properties. The yield and ultimate strengths tell us how much stress a material can withstand, and are often used to define failure.

Ductility tells us how much plastic deformation a material undergoes before fracture.  Brittle materials fracture at very small strains, and can fail catastrophically.

Toughness tells us how much energy a material can absorb before fracture. It is closely linked to both strength and ductility.

Buckling is a failure mode that occurs in columns and other members that are loaded in compression. It is a sudden change deformation that occurs at a certain critical load.

In this video we explore some key topics relating to buckling, including Euler's formula, the effects of end conditions, and other aspects like the effect of column slenderness, inelastic buckling and the buckling of shells and plates.