1. COLUMNS = Slenderness Ratio r = Least radius of gyration, inches
SHORT COLUMNS
LONG COLUMNS
Fail by crushing, cracking
Fail by buckling
= Slenderness Ratio
r = Least radius of gyration, inches
E = Modulus of elasticity, ksi
Fy = Yield strength of steel, ksi

2. Fe = Euler’s Buckling Stress, ksi
CRITICAL
STRESS, ksi
(Fcr)
SHORT COLUMNS
LONG COLUMNS
SLENDERNESS RATIO

3. Pn = Nominal Strength (Failure Strength) of Column = Fcr. Ag, kips
Design strength of column = 0.9 x Pn
FOR LRFD
DESIGN STRENTH DESIGN LOAD
Pn Pu
= Resistance Factor for Compression, 0.9

4. Fixed
Pin
Free

5. EFFECTIVE LENGTH FACTOR , K
RECOMMENDED VALUES OF
EFFECTIVE LENGTH FACTOR , K
POINT OF INFLECTION
PIN
FIXED
FIXED
FIXED
PIN
PIN
K = 0.65
K = 1.0
K = 0.8

6. FREE TO ROTATE & TRANSLATE
FIXED
K = 2.1

7. PROBLEM # 1
Determine the available strength of the compression member shown in Figure 1, in each of the following ways:
Use AISC Equation E3-2 or E3-3. Compute both the design strength for LRFD and the allowable strength for ASD.
Use table 4-22 from Part 4 of the Manual. Compute both the design strength for LRFD and the allowable strength for ASD.
FIXED
HSS 10x6x ½
ASTM A500,
Grade B steel
(Fy = 46ksi)
Figure 1
K = 0.65
FIXED

8. PROBLEM # 1 Figure 1 Find Slenderness Ratio
FIXED OK
2) Find Euler’s Buckling Stress
HSS 10x6x ½
ASTM A500,
Grade B steel
(Fy = 46ksi)
3) Find if Short or Long Column
K = 0.65
SHORT COLUMN
FIXED
4) Find Fcr
Figure 1
Fcr

9. PROBLEM # 1 5) Design Strength of Column = 0.9 x Fcr x Ag
= 0.9 x x 13.5
= kips
Page # 4-31
Effective length
KL = 0.65 x 15 = 9.75’
*By interpolation = 486 -
= 474 kips

10. PROBLEM # 1
Page # 4-319
Load = 35.2 x 13.5
= kips

11. For the conditions shown in Figure 1, use LRFD and
PROBLEM # 2
For the conditions shown in Figure 1, use LRFD and
D = 90k
L= 260k
Select a W12 of A992 steel.
Select a steel pipe.
Select a square HSS.
Select a rectangular HSS.
FLANGES
WEB
Pu = 1.2D + 1.6L
= 1.2 x x 260
= 524 kips
KL = 0.65 x 15.33’
= 9.97’
A 992
STEEL
W12
PIPE, RECTANGULAR HSS, SQUARE HSS
Figure 1

12. PROBLEM # 2
W12
Page # 4-18

13. PROBLEM # 2 W12 COLUMN DESIGNATION WEIGHT (lbs/ft) LOAD CAPACITY
Pn (kips)
STRENGTH REQUIRE (Pu)
W12 53
590
524 kips

14. PROBLEM # 2
ROUND HSS
Page # 4-64

15. PROBLEM # 2
ROUND HSS
Page # 4-65

16. PROBLEM # 2
ROUND HSS
Page # 4-65

17. PROBLEM # 2
ROUND HSS
Page # 4-66

18. PROBLEM # 2 ROUND HSS COLUMN DESIGNATION WEIGHT (lbs/ft) LOAD CAPACITY
Pn (kips)
STRENGTH REQUIRE (Pu)
HSS x0.375
62.6
630
524 kips
HSS x0.312
52.3
528
HSS x0.375
54.6
545
HSS x0.500
54.8
531

19. PROBLEM # 2
SQUARE HSS
Page # 4-48

20. PROBLEM # 2
SQUARE HSS
Page # 4-49

21. PROBLEM # 2
SQUARE HSS
Page # 4-51