Lecture 11 - Concrete - Design
Type Lecture
Date @November 23, 2023
SIZING GUIDELINES.pdf https://www.youtube.com/watch?
Materials v=R6U9B_zQZgk&t=1988s&ab_channel=ShannonHilchie
Reviewed
Load Sharing
Transformed Sections
Composite Action
Concrete Columns
Concrete Beams
Load Sharing
When two element or materials are arranged so that they mutually support load they are
said to be sharing the load. The proportion of load that each resists is proportional to the
stiffness of that element or material. Load will follow the path of greatest resistance (or
the stiffest element)
Multiple elements supporting the same load share it based on stiffness
The load likes the path with the MOST resistance.
What’s going to take most of the load?
Lecture 11 - Concrete - Design 1
, Steel rod wrapped in Play-doh
Steel Rod because steel is stiffer
Even though it has way less area
Steel rod wrapped in Wood
Not obvious. Steel is still stiffer, but the area of the wood
is larger
Load Sharing
How would a concrete and steel column share load?
To share load at all, they need to move (squash) together
Remember our basic formulas…
σ = F /Aor F = σ ∗ A ε = ΔL/L E = σ/εor σ = E ∗ ε
We can substitute things into each other, giving:
F = EAε where E and A are for each material.
ε has to be the same (strain) because they are moving together!
So for each material:
F s = (EA)sεand F c = (EA)cε
Load Sharing cont.
We want this related to the total load:
F = F s + F c
F s = (EA)sε + (EA)cε
Lecture 11 - Concrete - Design 2
, F = ε[(EA)s + (EA)c)]
F = εΣ(EA)
Σ(EA) is the axial stiffness of the combined (total) system
Rearranging F = εΣ(EA)…
ε = F /Σ(EA)
We can plug this back in to
F s = (EA)sεand F c = (EA)cε
F s = F ∗ (EA)s/Σ(EA)and F c = F ∗ (EA)c/Σ(EA)
Load Sharing Example
We have a steel HSS152x152x9.5 filled with concrete. What % of load does each
portion take if Ec = 30,000MPa?
Steel
Es = 200,000 MPa
Asteel = 5210 mm2
Esteel = 200,000 MPa
EAs = 200,000*5210 = 1.04x109 N
Concrete
E = 300,000 Pa
Aconc = (152-9.52)(152-9.52) = 17,689 mm2
Econc = 30,000 MPa
EAc = 30,000*17,689 = 0.531x109 N
ΣEA = 1.04x109 + 0.531x109 = 1.571x109 N
Lecture 11 - Concrete - Design 3
Type Lecture
Date @November 23, 2023
SIZING GUIDELINES.pdf https://www.youtube.com/watch?
Materials v=R6U9B_zQZgk&t=1988s&ab_channel=ShannonHilchie
Reviewed
Load Sharing
Transformed Sections
Composite Action
Concrete Columns
Concrete Beams
Load Sharing
When two element or materials are arranged so that they mutually support load they are
said to be sharing the load. The proportion of load that each resists is proportional to the
stiffness of that element or material. Load will follow the path of greatest resistance (or
the stiffest element)
Multiple elements supporting the same load share it based on stiffness
The load likes the path with the MOST resistance.
What’s going to take most of the load?
Lecture 11 - Concrete - Design 1
, Steel rod wrapped in Play-doh
Steel Rod because steel is stiffer
Even though it has way less area
Steel rod wrapped in Wood
Not obvious. Steel is still stiffer, but the area of the wood
is larger
Load Sharing
How would a concrete and steel column share load?
To share load at all, they need to move (squash) together
Remember our basic formulas…
σ = F /Aor F = σ ∗ A ε = ΔL/L E = σ/εor σ = E ∗ ε
We can substitute things into each other, giving:
F = EAε where E and A are for each material.
ε has to be the same (strain) because they are moving together!
So for each material:
F s = (EA)sεand F c = (EA)cε
Load Sharing cont.
We want this related to the total load:
F = F s + F c
F s = (EA)sε + (EA)cε
Lecture 11 - Concrete - Design 2
, F = ε[(EA)s + (EA)c)]
F = εΣ(EA)
Σ(EA) is the axial stiffness of the combined (total) system
Rearranging F = εΣ(EA)…
ε = F /Σ(EA)
We can plug this back in to
F s = (EA)sεand F c = (EA)cε
F s = F ∗ (EA)s/Σ(EA)and F c = F ∗ (EA)c/Σ(EA)
Load Sharing Example
We have a steel HSS152x152x9.5 filled with concrete. What % of load does each
portion take if Ec = 30,000MPa?
Steel
Es = 200,000 MPa
Asteel = 5210 mm2
Esteel = 200,000 MPa
EAs = 200,000*5210 = 1.04x109 N
Concrete
E = 300,000 Pa
Aconc = (152-9.52)(152-9.52) = 17,689 mm2
Econc = 30,000 MPa
EAc = 30,000*17,689 = 0.531x109 N
ΣEA = 1.04x109 + 0.531x109 = 1.571x109 N
Lecture 11 - Concrete - Design 3
