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Derick Francis
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1 Assignment 10 Problem 5.46 LRFD First, select the lightest weight W14 column. Use the recommended design value for K for the pinned-fixed support condition specified (ref. Commentary, Appendix 7, AISC Table C-A-7.1, p ). Compute the column effective length KL using the recommended design value for K. Compute the LRFD factored load. P u = 1.2 D L Using AISC Table 4-1, select the lightest W14 section that has a value of φ c P n for the computed effective length KL that is no less than the value computed for P u. You will need to interpolate between the rows to determine the value of φ c P n. Next, design the column base plate. From Table 1-1 of the AISC Manual, list the pertinent section properties for the selected column section (d, b f ). Determine the base plate area using the following equation (φ c = 0.65). A 1 = P u /[φ c 0.85 f c (A 2 /A 1 ) 1/2 ] (A 2 /A 1 ) 1/2 = 1.0 since A 2 is said to be approximately the same size as the column base plate Check the minimum required area (A 1 ) min for the base plate. - A 1 may not be less than the depth of the column times its flange width (i.e. d x b f ). If (A 1 ) min = d b f > required A 1 (calculated above), use (A 1 ) min as the area of the base plate. Otherwise, use A 1 as the area of the base plate. Compute the base plate dimensions B and N. - Since this is a square base pate B = N. B = N = (A 1 ) 1/2 (Round up to the nearest inch.) Check the bearing strength φ c P p of the concrete using the following equation. φ c P p = φ c 0.85 f c A 1 (A 2 /A 1 ) 1/2 φ c = 0.65 f c = the specified concrete compression strength A 1 = B x N (based on the rounded dimensions determined above). (A 2 /A 1 ) 1/2 = 1.0 Compare the bearing strength of the concrete with the factored column load P u. You should find that φ c P p > P u. Compute the required base plate thickness using the following equation. t min = l (2 P u /0.9 F y B N) 1/2 (Round up to the nearest quarter of an inch.) l = max (m. n, or λn ) (i.e. l is the largest of the values of m, n, or n ) m = (N 0.95 d)/2 n = (B b f )/2 Page 1 of 6

2 n = ¼ (d b f ) 1/2 λ = 1 B = N = rounded dimensions of the base plate determined previously F y = the minimum specified yield strength of the A36 steel used in the base plate (cf. AISC Table 2-4) Specify the final base plate dimensions. Use the following format: PL B x N x t (A36) ASD First, select the lightest weight W14 column. Use the recommended design value for K for the pinned-fixed support condition specified (ref. Commentary, Appendix 7, AISC Table C-A-7.1, p ). Compute the column effective length KL using the recommended design value for K. Compute the ASD critical load combination. P a = D + L Using AISC Table 4-1, select the lightest W14 section that has a value of P n /Ω c for the computed effective length KL that is no less than the value computed for P a. You will need to interpolate between the rows to determine the value of P n /Ω c. Next, design the column base plate. From Table 1-1 of the AISC Manual, list the pertinent section properties for the selected column section (d, b f ). Determine the base plate area using the following equation (Ω c = 2.31). A 1 = Ω c P a /[0.85 f c (A 2 /A 1 ) 1/2 ] (A 2 /A 1 ) 1/2 = 1.0 since A 2 is said to be approximately the same size as the column base plate Check the minimum required area (A 1 ) min for the base plate. - A 1 may not be less than the depth of the column times its flange width (i.e. d x b f ). If (A 1 ) min = d b f > required A 1 (calculated above), use (A 1 ) min as the area of the base plate. Otherwise, use A 1 as the area of the base plate. Compute the base plate dimensions B and N. - Since this is a square base pate B = N. B = N = (A 1 ) 1/2 (Round up to the nearest inch.) Check the bearing strength P p /Ω c of the concrete using the following equation. P p /Ω c = (1/Ω c ) [0.85 f c A 1 (A 2 /A 1 ) 1/2 ] Ω c =2.31 f c = the specified concrete compression strength A 1 = B x N (based on the rounded dimensions determined above). (A 2 /A 1 ) 1/2 = 1.0 Compare the bearing strength of the concrete with the critical column load combination P a. You should find that P p /Ω c > P a. Page 2 of 6

3 Compute the required base plate thickness using the following equation. t min = l (3.33 P a /F y B N) 1/2 (Round up to the nearest quarter of an inch.) l = max (m. n, or λn ) (i.e. l is the largest of the values of m, n, or n ) m = (N 0.95 d)/2 n = (B b f )/2 n = ¼ (d b f ) 1/2 λ = 1 B = N = rounded dimensions of the base plate determined previously F y = the minimum specified yield strength of the A36 steel used in the base plate (cf. AISC Table 2-4) Specify the final base plate dimensions. Use the following format: PL B x N x t (A36) Problem 5.50 LRFD Compute the LRFD factored load. P u = 1.2 D L Using AISC Table 4-11, select the lightest angle that has a value of φ c P n for the given effective length KL that is no less than the value computed for P u. This angle will be checked to determine if it has adequate load bearing capacity to satisfy the provisions of Specification Section E5. From Table 1-7 of the AISC Manual, list the pertinent section properties for the selected angle section (A and r x ). Check the ratio b/t to determine if Section E4 or E5 must be used. If b/t > 20, Section E4 is to be used, otherwise Section E5 will be used. b = the length of the angle leg t = the angle thickness You should find the b/t ratio less than 20, and Section E5 must be used. Compute the actual slenderness ratio KL x /r x and compare with the limiting value of 80. Then compute the value of the effective slenderness ratio KL/r that will be used to compute F e from Equation E3-4. If KL x /r x 80, then use Equation E5-1 to determine the effective slenderness ratio KL/r. If KL x /r x > 80, then use Equation E5-2 to determine the effective slenderness ratio KL/r. Compute F e using Equation E3-4. Determine whether Equation E3-2 or E3-3 is the appropriate equation to use in determining F cr by comparing effective slenderness ratio KL/r with the limiting value 4.71(E/F y ) 1/2. If KL/r 4.71(E/F y ) 1/2, then use Equation E3-2 to compute F cr. If KL/r > 4.71(E/F y ) 1/2, then use Equation E3-3 to compute F cr. Page 3 of 6

4 Compute the nominal strength P n of the single angle column by using the following equation. P n = F cr A g A g = the area for the single angle taken from AISC Table 1-7 Compute the LRFD design strength φ c P n and compare with the LRFD factored load P u. If φ c P n P u, then the selected single angle column section is adequate. If φ c P n < P u, then the selected single angle column section is not adequate. A larger angle section should be selected and checked following the procedure outlined above. Specify the final selection. ASD Compute the ASD critical load combination. P a = D + L Using AISC Table 4-11, select the lightest angle that has a value of P n /Ω c for the given effective length KL that is no less than the value computed for P a. This angle will be checked to determine if it has adequate load bearing capacity to satisfy the provisions of Specification Section E5. From Table 1-7 of the AISC Manual, list the pertinent section properties for the selected angle section (A and r x ). Check the ratio b/t to determine if Section E4 or E5 must be used. If b/t > 20, Section E4 is to be used, otherwise Section E5 will be used. b = the length of the angle leg t = the angle thickness You should find the b/t ratio less than 20, and Section E5 must be used. Compute the actual slenderness ratio KL x /r x and compare with the limiting value of 80. Then compute the value of the effective slenderness ratio KL/r that will be used to compute F e from Equation E3-4. If KL x /r x 80, then use Equation E5-1 to determine the effective slenderness ratio KL/r. If KL x /r x > 80, then use Equation E5-2 to determine the effective slenderness ratio KL/r. Compute F e using Equation E3-4. Determine whether Equation E3-2 or E3-3 is the appropriate equation to use in determining F cr by comparing effective slenderness ratio KL/r with the limiting value 4.71(E/F y ) 1/2. If KL/r 4.71(E/F y ) 1/2, then use Equation E3-2 to compute F cr. If KL/r > 4.71(E/F y ) 1/2, then use Equation E3-3 to compute F cr. Compute the nominal strength of the single angle column by using the following equation. P n = F cr A g Page 4 of 6

5 A g = the area for the single angle taken from AISC Table 1-7 Compute the ASD allowable strength P n /Ω c and compare with the ASD critical load combination P a. If P n /Ω c P a, then the selected single angle column section is adequate. If P n /Ω c < P a, then the selected single angle column section is not adequate. A larger angle section should be selected and checked following the procedure outlined above. Specify the final selection. Problem 5.54 From Table 1-8 of the AISC Manual, list the pertinent section properties for the given WT6 x 22.5 column member (i.e. A, t f, b f /2t f, d/t w, I x, r x, y, I y, r y, and J). Check for slender elements using AISC Table B4.1a. For the flange, use Case 1. Compare b f /2t f with the limiting value of 0.56(E/F y ) 1/2. - You should find that the flange is not slender. For the stem, use Case 4. Compare d/t w with the limiting value of 0.75(E/F y ) 1/2. - You should find that the stem is not slender. Determine the nominal strength of the column for flexural buckling using Specification Section E3. Determine the controlling slenderness ratio: compute KL x /r x and KL y /r y. K = 1.0 KL x = KL y = the given effective length r x, r y = values taken from AISC Table 1-8 You should find that KL x /r x is the larger value and controls. Since KL x /r x is the controlling slenderness ratio, compute F e (more specifically F ex ) using Equation E3-4. E = 29,000 ksi KL/r = KL x /r x (as previously determined) Determine whether Equation E3-2 or E3-3 is the appropriate equation to use in determining F cr by comparing KL x /r x with the limiting value 4.71(E/F y ) 1/2. - If KL x /r x 4.71(E/F y ) 1/2, then use Equation E3-2 to compute F cr. - If KL x /r x > 4.71(E/F y ) 1/2, then use Equation E3-3 to compute F cr. Next, determine the nominal strength of the column for flexural-torsional buckling using Specification Section E4. Ultimately, Equation E4-2 will be used to compute F cr once values for F cry, F crz, and H are determined. Compute F ey using Equation E Use the value for KL y /r y that was previously determined. Page 5 of 6

6 - The value F ey will be used as the value for F e in either Equation E3-2 or E3-3, whichever equation is determined appropriate. Determine whether Equation E3-2 or E3-3 is the appropriate equation to use in determining F cr (more specifically F cry ) by comparing KL y /r y with the limiting value 4.71(E/F y ) 1/2. - If KL y /r y 4.71(E/F y ) 1/2, then use Equation E3-2 to compute F cr (more specifically F cry ). - If KL y /r y > 4.71(E/F y ) 1/2, then use Equation E3-3 to compute F cr (more specifically F cry ). Determine F crz. - Compute r o 2 : r o 2 = x o 2 + y o 2 + (I x + I y )/A g Equation E4-11 x o = 0 (The shear center of the tee is located at the intersection of the stem and the flange.) y o = y - t f /2 (Values for y and t f are taken from AISC Table 1-8.) I x, I y = values taken from AISC Table 1-8 A g = area of the WT6 x 22.5 (AISC Table 1-8) - Compute H using Equation E Compute F crz using Equation E4-3. G = 11,200 ksi (Specification Section E4, listed after Equation E4-9) J, A g = values taken from AISC Table 1-8 Compute F cr using Equation E4-2. Compare the two values of F cr computed for flexural buckling and flexural-torsional buckling. The nominal strength of the column P n is based on the smaller of the two values determined for F cr for flexural buckling and flexural-torsional buckling. Compute the nominal strength of the column using the following equation. P n = F cr A g F cr = the smaller of the two values previously determined A g = the area for the WT6 x 22.5 taken from AISC Table 1-8 Compute the LRFD design strength (φ c P n ) and the ASD allowable strength (P n /Ω c ), φ c = 0.90 and Ω c = Note: These values should compare favorably with the values in AISC Table 4-7. Page 6 of 6

UNIVERSITY OF AKRON Department of Civil Engineering

UNIVERSITY OF AKRON Department of Civil Engineering 4300:401-301 July 9, 2013 Steel Design Sample Quiz 2 1. The W10 x 54 column shown has both ends pinned and consists of A992 steel (F y = 50 ksi, F u