Question

m Review Learning Goal: To use the formula for the critical load, i.e., the Euler buckling load, for pin-supported columns to calculate various parameters of columns. A column is made from a rectangular bar whose cross section is 5.5 cm by 9.1 cm . If the height of the column is 2 m, what is the maximum load it can support? The material has E = 200 GPa and Oy = 250 MPa Express your answer with appropriate units to three significant figures. View Available Hint(s) Ideally, a column that is perfectly straight and has an axial load applied exactly at the centroid of its cross section will not yield until the internal normal stress reaches the yield stress of the material. Real-world columns, however, are subject to small asymmetries, whether due to irregularities of shape or just lateral vibrations. When the axial load is large enough relative to the length of the column, such asymmetries cause the column to become unstable and buckle. It bends and continues bending until it fails. Tommplates Symbols uado redo reset keyboard shortcuts help, Value Units Rnax= Submit Previous Answers * Incorrect; Try Again; 4 attempts remaining Part B - Maximum length The load required to cause buckling depends on how the column is attached to its supports. The maximum or critical load for a column of length L that is pin EI supported at both ends is Per = TZ. A circular column with diameter 9.8 cm is to support a vertical load of 700 kN . What is the maximum length the column can have if it is pin supported at both ends? The material has E = 200 GPa . Assume the material does not yield. Express your answer with appropriate units to three significant figures. A factor of safety is used to account for uncertainties in material properties and dimensions. The factor of saftey is the ratio of the failure load to the allowable load, or the ratio of the maximum design load to the maximum expected load. View Available Hint(s) Toonplates Symbol Lado redo reset keyboard shortcuts help Lmax= Value Units Submit Part C - Required diameter A solid circular steel column with a height of 2 m needs to support a vertical load of 960 kN. What is the minimum diameter required if the factor of safety for buckling is FS = 2.5 and the material has E = 200 GPa ? Assume the material does not yield. Express your answer with appropriate units to three significant figures. View Available Hint(s) Tonplates Symbol uado redo reset keyboard shortcuts help

Answer 1

- Vield stres Parnas Rectangular bar = 5.5cm X 9.1 cm (h) height of Column, la am material properties E= 200 GPa dy = 250 mpa Calculate momenteel inertia of Reekingular bu Elastic modulus I = 1-26x10-6 mt 12 Buckling load Critical load, Pap = AREI A²x200x1097*1.26x10-6 (23) = 621.8X103N I Per = 621 KN) Parts diameter of circular Celumm, D=9.8cm Vertical load, P = 700 kN , Yound modulus. E= 200 Gp AZ ET I o4 for ein war section Troxlo? Na x 200110% lax 19.08) * maximum length of belumn = 3.57 m Inay

Paulo t Length of falumb L= am Vertical load applied, p = factor of safety for Bucking f5= 2.5 Young (Elastic) inadurley, E= 2000 Pa Critical lead Per = PX8.5 = 960 kN x2.5 = (960x2.5X1033 N for einalen shaft Critical load, Po A² EJ gresta d e ghentic 64 12 groxlox2.5 = *²x200x10²x I dt 64 . (2) 2 - amin a minimum diameter, dan ~ 0.0 998 0.1m - 0.100 m