Chapter 10 | Solution to Problems | Columns | Mechanics of Materials

Solution to Problems | Chapter 10 | Columns
Textbook: Mechanics of Materials, 7th Edition, by Ferdinand Beer, E. Johnston, John DeWolf and David Mazurek
Lecture by: Dr. Atta ur Rehman Shah

Content:

Problem 10.17: A column of 22-ft effective length is made by welding two 9 x 0.5-in. plates to a W8 x 35 as shown. Determine the allowable centric load if a factor of safety of 2.3 is required. Use E = 29 x 106 psi.

Problem 10.21: The uniform brass bar AB has a rectangular cross section and is supported by pins and brackets as shown. Each end of the bar can rotate freely about a horizontal axis through the pin, but rotation about a vertical axis is prevented by the brackets. (a) Determine the ratio b/d for which the factor of safety is the same about the horizontal and vertical axes. (b) Determine the factor of safety if P = 1.8 kips , L = 7 ft, d = 1.5 in., and E = 29 x 106 psi .

Problem 10.23: A 1-in.-square aluminum strut is maintained in the position shown by a pin support at A and by sets of rollers at B and C that prevent rotation of the strut in the plane of the figure. Knowing that LAB = 3 ft, LBC = 4 ft , and LCD = 1 ft, determine the allowable load P using a factor of safety with respect to buckling of 3.2. Consider only buckling in the plane of the figure and use E = 10.4 x 106 psi.

Problem 10.24: Column ABC has a uniform rectangular cross section withb = 12 mm and d = 22 mm. The column is braced in the xz plane at its midpoint C and carries a centric load P of magnitude 3.8 kN. Knowing that a factor of safety of 3.2 is required, determine the largest allowable length L. Use E = 200 GPa.

Problem 10.36: A brass pipe having the cross section shown has an axial load P applied 5 mm from its geometric axis. Using E = 120 GPa, determine (a) the load P for which the horizontal deflection at the midpoint C is 5 mm, (b) the corresponding maximum stress in the column.

Problem 10.39: The line of action of the axial load P is parallel to the geometric axis of the column and applied at a point located on the x-axis at a distance e = 12 mm from the geometric axis of the W310 x 60 rolled-steel column BC. Assuming that L = 7.0 m and using E = 200 GPa, determine (a) the load P for which the horizontal deflection of the midpoint C of the column is 15 mm, (b) the corresponding maximum stress in the column.