Materials and Civil Engineering
1. Draw and explain a stress-strain curve for steel. Where is the elastic limit? The yield point? What are stress and strain? How would work be defined on the stress-strain curve?
Solution:
Stress vs. Strain curve for structural steel. Reference numbers are:
1 - Ultimate Strength
2 - Yield Strength(elastic limit)
3 - Rupture
4 - Strain hardening region
5 - Necking region
stress, derived from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample, i.e. elongation, compression, or distortion
Work is the area under the curve.
2. Compare and contrast a stress-strain curve for steel with a similar curve of concrete.
Solution:
Stress vs. Strain curve for brittle material (concrete)
1 Ultimate Strength
2 Rupture
3. What effect does varying pH have on metals?
Solution:
4. Why is glass more difficult to break when it has been tempered? Describe what occurs within the glass.
Solution:
Tempering is a stress relief annealing which causes defects in the glass to diffuse through out the material rather than concentrating at a particular location. It increases the ductility and it allows it to absorb more plastic deformation before failing and therefore is harder to break.
5. What is “Young’s Modulus”? What is its approximate value for steel?
Solution:
Young's modulus (E) is a measure of the stiffness of an isotropic elastic material. E= 190-210GPa = 30,000,000psi for steel.
6. Describe the pros and cons of castings versus forgings.
Solution:
Casting: good for intricate shapes, finish is rough, tolerance is poor
Forging: Excellent strength, high toughness, excellent tolerances, shapes are limited
7. Given an I-beam, what types of forces are acting at the point of load on this beam? How do you find these forces?
Solution:
Shear and Flexural Stress.
Shear=
Flexural Stress=
V shear from the shear diagram
I moment of inertia
b cross-section thickness
Q first moment
s stress due to bending
M bending moment
I moment of inertia
y distance from the neutral axis
n ratio of moduli of elasticity
8. Draw the shear and moment diagrams for this beam.
Solution:
9. Define the following and explain what quantities they compare. (Give units where applicable)
a. Hooke’s Law
b. Poisson’s Ratio
Solution:
Hooke's law :
A generalization applicable to all solid materials, stating that stress is directly proportional to strain and expressed as where E is the modulus of elasticity, or Young's modulus, in pounds per square inch. The constant relationship between stress and strain applies only to stress below the proportional limit.
Poisson’s Ratio:
The ratio of the transverse contracting strain to the elongation strain when a rod is stretched by forces which are applied at its ends and which are parallel to the rod's axis.
Assuming that the material is compressed along the axial direction:
where
ν is the resulting Poisson's ratio,
is transverse strain,
is axial strain
10. Define “cold working”. What goes on within the material? What happens during “annealing”? Give physical properties.
Cold working: cold work is the strengthening of a material by, macroscopically speaking, plastic deformation (which has the nano-scopic effect of increasing the material's dislocation density). As the material becomes increasingly saturated with new dislocations, more dislocations are prevented from nucleating (a resistance to dislocation-formation develops).
Annealing: The process used to render glass, iron, etc., less brittle, performed by allowing them to cool very gradually from a high heat. Annealing is used to induce ductility, relieve internal stresses, refine the structure and improve cold working properties
11. Draw the shear and moment diagrams for this uniformly loaded beam.
Solution:
Shear:
Moment: