2. (a) Figure Q2 shows a rigid-jointed frame ABCD fixed at C, pinned at D and subjected to an axial force P at the free end A. (i) Plot the buckled shape of the frame and estimate the effective length factor k₂ of column AB. Then simplify the frame into a column with an equivalent flexural stiffness at B representing those of beams BC and BD. (ii) Establish a second-order differential equation for column AB considering second order effect from the axial force P. Apply appropriate boundary conditions to column AB and obtain the governing equation for column stability. (iii) Hence, obtain the effective length factor ke for column AB and compare it with the estimated value from Part (i). Comment on the difference if any. (14 Marks) (b) (i) Column AB in Figure Q2 is of length L =1.5 m and is restrained from minor axis buckling and lateral torsional buckling. Based on the estimated or calculated value of effective length factor ke for major-axis buckling from Part (a), find the maximum value of P if an engineer decides to use 152 × 152 UKC 30 kg/m Grade S355 plastic section for column AB in Figure Q2. Please state any assumptions in the design. Section classification and cross-section resistance checks are not required. (ii) Suggest a practical method to increase the major-axis buckling resistance of column AB. (11 Marks) UKC steel section: 152 × 152 UKC 30 kg/m Grade S355, fyd = 355 N/mm² Class 1 for flange and web E₁ = 210 kN/mm², h = 157.6 mm, b = 152.9 mm, tw = 6.5 mm, t = 9.4 mm, r = 7.6 mm, d=123.6 mm, ly = 1750 cm², Iz = 560 cm², Welly = 222 cm³, Welz -73.3 cm³, Wpl.y = 248 cm³, Wplz = 112 cm³, A₂ = 38.3 cm² P УШЕЙШОЙ: usbous cobluёр уст вобука до де паводле доспшен изиквий десинойся прекар при L ΕΙ ΕΙ Β ΕΙ L Figure Q2 D
2. (a) Figure Q2 shows a rigid-jointed frame ABCD fixed at C, pinned at D and subjected to an axial force P at the free end A. (i) Plot the buckled shape of the frame and estimate the effective length factor k₂ of column AB. Then simplify the frame into a column with an equivalent flexural stiffness at B representing those of beams BC and BD. (ii) Establish a second-order differential equation for column AB considering second order effect from the axial force P. Apply appropriate boundary conditions to column AB and obtain the governing equation for column stability. (iii) Hence, obtain the effective length factor ke for column AB and compare it with the estimated value from Part (i). Comment on the difference if any. (14 Marks) (b) (i) Column AB in Figure Q2 is of length L =1.5 m and is restrained from minor axis buckling and lateral torsional buckling. Based on the estimated or calculated value of effective length factor ke for major-axis buckling from Part (a), find the maximum value of P if an engineer decides to use 152 × 152 UKC 30 kg/m Grade S355 plastic section for column AB in Figure Q2. Please state any assumptions in the design. Section classification and cross-section resistance checks are not required. (ii) Suggest a practical method to increase the major-axis buckling resistance of column AB. (11 Marks) UKC steel section: 152 × 152 UKC 30 kg/m Grade S355, fyd = 355 N/mm² Class 1 for flange and web E₁ = 210 kN/mm², h = 157.6 mm, b = 152.9 mm, tw = 6.5 mm, t = 9.4 mm, r = 7.6 mm, d=123.6 mm, ly = 1750 cm², Iz = 560 cm², Welly = 222 cm³, Welz -73.3 cm³, Wpl.y = 248 cm³, Wplz = 112 cm³, A₂ = 38.3 cm² P УШЕЙШОЙ: usbous cobluёр уст вобука до де паводле доспшен изиквий десинойся прекар при L ΕΙ ΕΙ Β ΕΙ L Figure Q2 D
Steel Design (Activate Learning with these NEW titles from Engineering!)
6th Edition
ISBN:9781337094740
Author:Segui, William T.
Publisher:Segui, William T.
Chapter10: Plate Girders
Section: Chapter Questions
Problem 10.7.9P
Related questions
Question
Transcribed Image Text:2.
(a) Figure Q2 shows a rigid-jointed frame ABCD fixed at C, pinned at D and
subjected to an axial force P at the free end A.
(i) Plot the buckled shape of the frame and estimate the effective length
factor k₂ of column AB. Then simplify the frame into a column with an
equivalent flexural stiffness at B representing those of beams BC and
BD.
(ii) Establish a second-order differential equation for column AB
considering second order effect from the axial force P. Apply
appropriate boundary conditions to column AB and obtain the
governing equation for column stability.
(iii) Hence, obtain the effective length factor ke for column AB and compare
it with the estimated value from Part (i). Comment on the difference if
any.
(14 Marks)
(b) (i) Column AB in Figure Q2 is of length L =1.5 m and is restrained from
minor axis buckling and lateral torsional buckling. Based on the
estimated or calculated value of effective length factor ke for major-axis
buckling from Part (a), find the maximum value of P if an engineer
decides to use 152 × 152 UKC 30 kg/m Grade S355 plastic section
for column AB in Figure Q2. Please state any assumptions in the
design. Section classification and cross-section resistance checks are
not required.
(ii) Suggest a practical method to increase the major-axis buckling
resistance of column AB.
(11 Marks)
UKC steel section:
152 × 152 UKC 30 kg/m Grade S355, fyd = 355 N/mm²
Class 1 for flange and web
E₁ = 210 kN/mm², h = 157.6 mm, b = 152.9 mm, tw = 6.5 mm, t = 9.4 mm,
r = 7.6 mm, d=123.6 mm, ly = 1750 cm², Iz = 560 cm², Welly = 222 cm³,
Welz -73.3 cm³, Wpl.y = 248 cm³, Wplz = 112 cm³, A₂ = 38.3 cm²
P
УШЕЙШОЙ: usbous cobluёр уст вобука до де паводле доспшен изиквий десинойся прекар при
L
ΕΙ
ΕΙ
Β ΕΙ
L
Figure Q2
D
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Steel Design (Activate Learning with these NEW ti…
Civil Engineering
ISBN:
9781337094740
Author:
Segui, William T.
Publisher:
Cengage Learning
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781305081550
Author:
Braja M. Das
Publisher:
Cengage Learning
Steel Design (Activate Learning with these NEW ti…
Civil Engineering
ISBN:
9781337094740
Author:
Segui, William T.
Publisher:
Cengage Learning
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781305081550
Author:
Braja M. Das
Publisher:
Cengage Learning
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Residential Construction Academy: House Wiring (M…
Civil Engineering
ISBN:
9781285852225
Author:
Gregory W Fletcher
Publisher:
Cengage Learning
Engineering Fundamentals: An Introduction to Engi…
Civil Engineering
ISBN:
9781305084766
Author:
Saeed Moaveni
Publisher:
Cengage Learning