axial force, deformation,buckling

The Cooper Union Name of Student:

Irwin S. Chanin School of Architecture ______________________________________

Arch 132 Structures II Spring Semester 2021

Thorsten Helbig, Associate Professor

Florian Meier, Instructor

Class Meets: Monday: 2:00PM-04:50PM (Zoom)

Assignment 2

1 of 6

Assignment 2: Axial Force, Deformation, Buckling

1) Determine the axial force N and the deformation ΔL of the steel rod shown below:

The Cooper Union Name of Student:

Irwin S. Chanin School of Architecture ______________________________________

Arch 132 Structures II Spring Semester 2021

Thorsten Helbig, Associate Professor

Florian Meier, Instructor

Class Meets: Monday: 2:00PM-04:50PM (Zoom)

Assignment 2

2 of 6

2) A) Determine the axial force N and the deformation ΔL of the W-profile shown below.

Determine the axial strength Pn of the section and compare with the load P. Do not consider

the possibility of buckling yet.

The Cooper Union Name of Student:

Irwin S. Chanin School of Architecture ______________________________________

Arch 132 Structures II Spring Semester 2021

Thorsten Helbig, Associate Professor

Florian Meier, Instructor

Class Meets: Monday: 2:00PM-04:50PM (Zoom)

Assignment 2

3 of 6

B) Now determine the critical Euler-buckling load Pcrit of the system and analyze whether a

buckling problem exists or not (buckling problem exists if Pcrit is lower than Pn). Be careful:

Consider buckling in both directions (around the section’s y-y and z-z axis)

The Cooper Union Name of Student:

Irwin S. Chanin School of Architecture ______________________________________

Arch 132 Structures II Spring Semester 2021

Thorsten Helbig, Associate Professor

Florian Meier, Instructor

Class Meets: Monday: 2:00PM-04:50PM (Zoom)

Assignment 2

4 of 6

C) How would you modify the system to prevent the buckling problem or at least improve the

Euler buckling strength (choose one)? Calculate the critical buckling load for the new system

(length, section and load remains the same, only support conditions change).

□

□

□

The Cooper Union Name of Student:

Irwin S. Chanin School of Architecture ______________________________________

Arch 132 Structures II Spring Semester 2021

Thorsten Helbig, Associate Professor

Florian Meier, Instructor

Class Meets: Monday: 2:00PM-04:50PM (Zoom)

Assignment 2

5 of 6

D) What other parameter could be changed in order to prevent buckling and how? Give 2

suggestions:

3) A) Determine the critical buckling load Pcrit of the system below and analyze whether a

buckling problem exists or not (buckling problem exists if Pcrit is lower than Pn).

The moment of Inertia for a round section can be calculated with:

𝐼𝑦 = 𝐼𝑧 = 𝜋

4 × 𝑅4 where R is the outer radius of the circle

The Cooper Union Name of Student:

Irwin S. Chanin School of Architecture ______________________________________

Arch 132 Structures II Spring Semester 2021

Thorsten Helbig, Associate Professor

Florian Meier, Instructor

Class Meets: Monday: 2:00PM-04:50PM (Zoom)

Assignment 2

6 of 6

B) The system is modified to a circular hollow profile. The profile is produced with the same

resources/tonnage of steel (same area A). Determine the new critical buckling load Pcrit of the

system below and analyze whether a buckling problem still exists or not.