Understanding Composite Materials

The development of composite materials over the last few decades has completely transformed how some of the most advanced enginering problems can be solved. But what is a composite material?

What is a composite material?

A composite is really just any material made from two or more distinct constituent materials. Usually one material, the dispersed phase, is contained within another, the matrix phase. The dispersed phase is what provides the desirable material properties, like improved strength or improved ductility. The matrix holds everything together and protects the dispersed phase from the environment.

The real strength of composites is that the dispersed and matrix materials can be carefully selected to develop a new material that has properties (mechanical, electrical, thermal, magnetic etc…) that have been tailored to suit a specific application.

What are the different types of composite materials?

Composites are often categorised according to the form of the dispersed phase. Common forms include:

  • particle-reinforced composites
  • short or chopped fiber-reinforced composites
  • continuous fiber-reinforced composites

Concrete is an example of a particle-reinforced composite. Fiberglass and carbon fiber-reinforced polymers (CFRP) are fiber-reinforced polymers composites.

But they are also categorised according the the type of matrix material:

  • polymer matrix composites (PMC)
  • ceramic matrix composites (CMC)
  • metal matrix composites (MMC)

The video below covers the different types of composite materials and how they are constructed and used in detail.

Understanding Composite Materials Read More »

Area Moment of Inertia Calculator

This calculator is used to calculate the area moment of inertia, or second moment of area, for a range of different beam cross-sections and bending axes. The area moment of inertia is a parameter that defines how much resistance the cross-section of a beam has to bending because of its geometry.

Circular Cross-Section | Bending axes pass through centroid
Rectangular cross-section
$I_{xx} = I_{yy} = \frac{\pi r^4}{4}$
Hollow Circular Cross-Section | Bending axes pass through centroid
Hollow circular cross-section
$I_{xx} = I_{yy} = \frac{\pi}{4} ({r}^4 - (r - t)^4)$
Rectangular Cross-Section | Bending axes pass through centroid
rectangle circular cross-section
$I_{xx} = \frac{bh^3}{12}$ $I_{yy} = \frac{b^3h}{12}$
I-Beam Cross-Section | Bending axes pass through centroid
rectangle circular cross-section
$I_{xx} = \frac{b(d+2t)^3}{12}-\frac{(b-t_w)d^3}{12}$ $I_{yy} = \frac{b^3t}{6}+\frac{{t_w}^3d}{12}$

Remember that the parallel axis theorem can be used to calculate $I$ for different bending axes. It states that the area moment of inertia about any axis $I_x$ can be calculated from the area moment of inertia about a parallel axis $I_{xc}$ that passes through the centroid of the cross-section, the area of the cross-section $A$ and the distance between the two axes $d$. Have a read of our page on the area moment of inertia to learn more about how the parallel axis theorem works.

Parallel Axis Theorem
$$I_x = I_{xc} + Ad^2$$

Related Topics

Area Moment of Inertia

The area moment of inertia describes how the material of a cross-section is distributed relative to a specific bending axis.

Buckling

Buckling is a sudden deflection that occurs in slender columns or members that are loaded in compression.

Area Moment of Inertia Calculator Read More »

Critical Buckling Force Calculator

This calculator is used to calculate the critical buckling force, the force at which a column will begin to buckle. You can play around with it to see how the different input parameters like Young’s modulus, second moment of area, column length and the column end conditions all affect how much force a column can carry.

Critical Buckling Force Calculator
Enter your cross-section properties, material, column length and select your end conditions to calculate the critical buckling force for your column.
Cross-section Image
Fixed-Fixed
Fixed-Fixed
Fixed-Pinned
Pinned-Pinned
Fixed-Free
Critical Buckling Force

The critical buckling force is calculated using Euler’s buckling formula, shown below. This equation and the calculator above do not include any safety factors. Have a read of our page on buckling to learn more about this equation and the buckling of columns.

Euler’s Buckling Formula
$$P_{cr}=\frac{\pi ^{2}EI}{{L_{e}}^{2}}$$

Related Topics

Buckling

Buckling is a sudden deflection that occurs in slender columns or members that are loaded in compression.

Torsion

Torsion is the twisting of an object caused by a moment applied about a longitudinal axis (torque).

Critical Buckling Force Calculator Read More »

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