Structure 4

Question 1

Young’s Modulus

Answer 1

Young’s Modulus is a formula which can be used to measure the elasticity of a material

Equation: E = Stress/Strain

Question 2

Adequate Strength

Answer 2

A beam or column that is part of an overall structure is designed so it can carry a force without it failing.

It has to be:

1. Sufficient in size
2. For the material used
3. Not ‘overstressed’ by the applied forces (External and Internal)

Example:

• Steel is 20x stronger than timber, meaning the same load can be carried on a smaller cross sectional area in a steel structure than in a timber one

Question 3

Simple Bending Theory

Answer 3

• Bending moments are independent of beam geometry and material character
• Geometry and material nature must take be taken into account to determine stresses and deformations
• Bending equation relates bending moment to stresses, material properties and cross sectional geometry
• Equation: σ/y = M/I = E/r

Question 4

Simple Bending Theory:

Beams

Answer 4

• The radius of curvature (r) is a measure of the deformation of the cross section of the beam
• As the radius of curvature decreases the greater the deformation of the beam

Bending in Beams

• Steel Beams: stretch and reach a plastic state at failure
• Timber Beams: tends to pull apart at its fibres
• Concrete Beams: is more brittle and tends to crack where there is most tension

Question 5

Second Moment of Area

Answer 5

I = bd³/12

Question 6

Stresses in Non-Rectangular Beams

Answer 6

• Rectangular beams tend to be less efficient than non rectangular ones e.g. I or H Beams
• The Second Moment of Area is calculated by using the formula I = bd³/12 (for a rectangular beam) and then subtracting the areas of material that is not part of the non-rectangular beam

Question 7

Stresses in Non-Rectangular Beams:

Non-Symmetrical Beams

Answer 7

• The centroid of non standard sections can be determined by subdividing the cross- sections into a series of rectangular components
• The total area of the section A, multiplied by the distance of the centroid to a given datum is the same as the sum of small areas, dA, multiplied by the respective distance to the centroid of dA