CIEG 214 Engineering Materials
Homework – Chapter 4 (1 - 6, 10 – 12)
1.​ What are the units of stress in the U.S. system of units and the SI system of units?
●​ US: Pounds per square inch (psi)
●​ SI: Pascals (Pa)
2.​ A l-in.-diameter steel bar is subjected to a tensile force of 30 kips. Determine the stress in the
bar.
3.​ If the bar in Problem 2 is 10 ft long, determine the elongation in the bar. The modulus of
elasticity of steel is 29E6 psi
4.​ Sketch the stress-strain diagram of low-carbon (mild) steel, showing all of its important parts,
and explain why steel should not be stressed beyond its yield stress.
●​ Permanent Deformation: If stress exceeds yield stress, the steel does not return to its
original shape when the load is removed
●​ Reduced Structural Integrity: Exceeding yield stress can weaken the material, leading to
deformation and potential failure
●​ Safety Concerns: In engineering applications (e.g., bridges, buildings), permanent
deformation can compromise safety and function
●​ Fatigue and Cracking: Repeated loading beyond yield can cause fatigue failure over time
5.​ Explain the modulus of elasticity. Which property of the material does it represent? Give the
approximate values of the modulus of elasticity of steel, concrete, and wood.
The modulus of elasticity (E), also called Young’s modulus, is a measure of how stiff or rigid a
material is. It tells us how much a material will stretch or compress when under stress, as long as
it stays within the elastic region (where it returns to its original shape after the load is removed).
Basically, the modulus of elasticity represents a material’s stiffness or how resistant it is to
deformation under stress. A higher modulus means the material is stiffer and doesn’t stretch
much, while a lower modulus means the material is more flexible.
Approximate Values of Modulus of Elasticity:
●​ Steel: ~29 × 10⁶ psi (200 GPa) → Super stiff, doesn’t stretch much
●​ Concrete: ~3-5 × 10⁶ psi (20-35 GPa) → Less stiff than steel, but still strong
●​ Wood: ~1-2 × 10⁶ psi (7-14 GPa) → Much more flexible compared to steel and concrete
6.​ Explain the difference between:
a)​ elasticity and modulus of elasticity of a material
Elasticity is a material’s ability to return to its original shape after being stretched or
compressed. Modulus of Elasticity (E) is a number that tells us how stiff a material is. A
high modulus means the material resists stretching, while a low modulus means it flexes
more easily. For example, steel and rubber are both elastic because they return to their
shape after a small stretch. But steel has a way higher modulus of elasticity, meaning it
barely stretches under stress, while rubber stretches a lot.
b)​ brittleness and ductility of materials
Brittle materials break suddenly without much warning. Ductile materials can bend or
stretch without snapping. For example, glass and concrete are brittle, they crack instead
of stretching. On the other hand steel and copper are ductile, they stretch and bend
without breaking right away.
10.​Explain what is bearing strength of a material and how it differs from the material’s
compressive strength.
The bearing strength of a material is the maximum stress a material can handle when a force is
applied to a small localized area. This tells us how well a material resists localized crushing or
failing. Compressive strength is the maximum stress a material can withstand when under
uniform compression. It measures a material’s ability to resist being squished under pressure.
11.​Explain the concept of buckling. Explain whether buckling would occur if a member is
subjected to bending. What measures do we adopt to prevent the buckling failure of building
components?
Buckling is when a slender structural member suddenly bends or collapses sideways due to
compressive forces. A slender structural member is a long and thin object that is more likely to
bend or buckle under compression instead of just shortening. It has a large length compared to its
width or thickness. For example, a tall, then column in a building. Buckling would not occur if a
member is subjected to bending because it typically occurs under compression. However,
bending can contribute to instability, especially if the member is both compressed and bent. A
beam that is mainly in bending won’t buckle, but if it’s long, thin, and under compression, it
could. To prevent buckling failure of building components, many measures are taken. Bracing is
when lateral supports are added to prevent side-to-side movement. Thicker and shorter columns
are used to reduce slenderness and make buckling less likely. Stronger materials like high
strength steel or reinforced concrete are used to resist buckling. I-beams and hollow tubes are
designed to resist buckling better.
12.​If the ultimate strength of a material is 6,000 psi and the factor of safety is 2.5, determine the
allowable stress of the material.