Lecture 8 - Steel - Design
Type Lecture
Date @October 26, 2023
https://www.youtube.com/watch?
Materials v=yW7HkxeKY54&ab_channel=ShannonHilchie STEEL COLUMN
TABLES.pdf STEEL BEAM TABLES.pdf
Reviewed
Stress and Strain- Recap
Steel – Axial Stress
Steel – Bending Stress
Steel Columns
Steel Beams
Stress and Strain and Modulus of Elasticity
If we know the stress, we can calculate the strain and vice versa
E = σ/ε σ = P /A ε = ΔL/L
Force Area
P = (EΔLA)/L A = (P L)/(EΔL)
Deformation Length
ΔL = (P L)/(EA) L = (EΔLA)/P
Lecture 8 - Steel - Design 1
, Full Stress Strain Curve – Steel
Euler – Bernoulli Theory
Step 1: Plane sections Step 2: To Step 3: In normal ranges, we
remain plane remain plane, the know stress and strain are
For beam-like elements, strain must vary proportional (Modulus of
transverse cross sections linearly with the Elasticity). Therefore, the stress
perpendicular to the distance from the must also vary linearly with it’s
neutral axis remain plane neutral axis. distance from the neutral axis.
and perpendicular to the
neutral axis.
Know the three Steps and what
the Stress Profile of a Rectangle
in Elastic Bending looks like
Lecture 8 - Steel - Design 2
, What does that give us? Knowing that our Stress profile can be written
as an analogous point load, and that equal and
If we look at a rectangle in bending,
opposite forces can be a couple, we can
just as it starts to yield at the
calculate the internal equilibrium of the beam…
extreme fibers, we have stress
profile that looks like this… But you don’t have to
What we’d calculate…
So, just as our steel starts to yield at the extreme fibers, we can figure out a relationship
between stress and moment
(we can calculate this, with our understanding of moments, eccentricity and couples…
but you don’t have to)
M = σS
S is a property based on the cross-section SHAPE of the member in elastic bending.
We can calculate or look up S
(for each shape, S is different… it’s a placeholder about the SHAPE)
Stress
Axial Stress Bending Stress (Elastic)
Lecture 8 - Steel - Design 3
Type Lecture
Date @October 26, 2023
https://www.youtube.com/watch?
Materials v=yW7HkxeKY54&ab_channel=ShannonHilchie STEEL COLUMN
TABLES.pdf STEEL BEAM TABLES.pdf
Reviewed
Stress and Strain- Recap
Steel – Axial Stress
Steel – Bending Stress
Steel Columns
Steel Beams
Stress and Strain and Modulus of Elasticity
If we know the stress, we can calculate the strain and vice versa
E = σ/ε σ = P /A ε = ΔL/L
Force Area
P = (EΔLA)/L A = (P L)/(EΔL)
Deformation Length
ΔL = (P L)/(EA) L = (EΔLA)/P
Lecture 8 - Steel - Design 1
, Full Stress Strain Curve – Steel
Euler – Bernoulli Theory
Step 1: Plane sections Step 2: To Step 3: In normal ranges, we
remain plane remain plane, the know stress and strain are
For beam-like elements, strain must vary proportional (Modulus of
transverse cross sections linearly with the Elasticity). Therefore, the stress
perpendicular to the distance from the must also vary linearly with it’s
neutral axis remain plane neutral axis. distance from the neutral axis.
and perpendicular to the
neutral axis.
Know the three Steps and what
the Stress Profile of a Rectangle
in Elastic Bending looks like
Lecture 8 - Steel - Design 2
, What does that give us? Knowing that our Stress profile can be written
as an analogous point load, and that equal and
If we look at a rectangle in bending,
opposite forces can be a couple, we can
just as it starts to yield at the
calculate the internal equilibrium of the beam…
extreme fibers, we have stress
profile that looks like this… But you don’t have to
What we’d calculate…
So, just as our steel starts to yield at the extreme fibers, we can figure out a relationship
between stress and moment
(we can calculate this, with our understanding of moments, eccentricity and couples…
but you don’t have to)
M = σS
S is a property based on the cross-section SHAPE of the member in elastic bending.
We can calculate or look up S
(for each shape, S is different… it’s a placeholder about the SHAPE)
Stress
Axial Stress Bending Stress (Elastic)
Lecture 8 - Steel - Design 3
