1. Flexural-Torsional Buckling
Bashar Behnam, Ph.D
Assistant Professor
Philadelphia University

2. Flexural-Torsional Buckling
This type of failure is caused by a combination of flexural buckling and torsional buckling.
This type of failure can occur only with unsymmetrical cross sections with one axis of symmetry (Singly Symmetrical shapes).
Structural Tee
WT, ST and MT
American Standard Channel

3. Flexural-Torsional Buckling
For singly symmetrical shapes:
y-axis is the axis of symmetry (regardless of the orientation of the member).
x-axis is the axis of no symmetry.
x-axis is subjected to flexural buckling only.
y-axis is subjected to 2 buckling actions: flexural buckling and torsional buckling. That’s why we call this failure mode “flexural-torsional buckling”.
Since there are two actions in flexural-torsional buckling, then the source of strength is a combination of flexural and torsional action.

4. Bending is associated with twisting
Flexural Buckling
Flexural-Torsional Buckling
Original Position
Axis of no symmetry
Original Position x z y
How to Quantify these two behaviors?
Bending is associated with twisting

5. Example 4.16
Compute the compressive strength of a C15  50 of A36 steel. The effective lengths with respect to the x, y, and z axes are each 13 feet. Use LRFD method.

6. Example 14.6 (cont.)
Compute the flexural buckling strength about x-axis (axis of no symmetry).
(Slenderness ratio)
ksi (elastic stress)
Determine whether the flexural buckling falls within the elastic range or inealstic range
since
 Elastic buckling and AISC Equation E3-3 applies

7. Example 14.6 (cont.)
ksi
note that is a reduction factor to account for the effects of initial crookness.
The nominal strength is
kips
Fcr
Critical stress (ksi) Ag
Gross cross-sectional Area (in2)

8. How to calculate the elastic stress?
Example 14.6 (cont.)
Compute the flexural-torsional buckling strength about the y-axis (axis of symmetry)
(Slenderness ratio)
Remember
since
 Inelastic buckling and AISC Equation E3-2 applies
How to calculate the elastic stress?
It is a 3-step process

9. Example 14.6 (cont.) ksi AISC equation E4-8 AISC equation E4-9 z ksi xG
shear modulus of elasticity, ksi. J
torsional constant, in4. Cw
warping constant, in4.
polar radius of gyration about the shear center, in. 1.
ksi
AISC equation E4-8 2.
AISC equation E4-9 x z y
Warping Torsional resistance
St. Venant Torsional resistance
ksi

10. Warping Constant

11. Example 14.6 (cont.) AISC Equation E4-5 ksi (elastic stress) ksi3.
AISC Equation E4-5
ksi (elastic stress)
ksi
The nominal strength is
kips
the smaller value controls, then flexural buckling strength controls and the nominal strength is kips

12. Example 14.6 (cont.) The design strength (factored) using LRFD method:
kips

13. Example 4.15
Compute the compressive strength of a WT12  81 of A992 steel. The effective lengths with respect to the x-axis is 25 ft 6 inches, the effective lengths with respect to y, and z axes are each 20 feet. Use LRFD method.

14. Example 14.5 (cont.)
Compute the flexural buckling strength about x-axis (axis of no symmetry).
(Slenderness ratio)
ksi (elastic stress)
Determine whether the flexural buckling falls within the elastic range or inealstic range
since
 Inelastic buckling and AISC Equation E3-2 applies

15. Example 14.5 (cont.)
ksi
Fcr
Critical stress (ksi) Ag
Gross cross-sectional Area (in2)
The nominal strength is
kips
Compute the flexural-torsional buckling strength about the y-axis (axis of symmetry)
Compute Fcry
(Slenderness ratio)

16. Example 14.5 (cont.) Remember since
 Inelastic buckling and AISC Equation E3-2 applies
ksi (elastic stress)
ksi
Because the shear center of a tee is located at the intersection of the
centerlines of the flange and the stem,

17. Example 14.5 (cont.)

18. Example 14.5 (cont.) The nominal strength is kips
the smaller value controls, then flexural buckling strength controls and the nominal strength is kips