Chapter 7 - Concentrically Loaded Compression Members
© 2006, 2008, 2011 T. Bartlett Quimby
As presented in Chapter 1, the homework problems involve the design of elements of three different structures plus some unrelated details. Please see the relevant links below for each structure. When completing the problems, consider both ASD and LRFD design philosophies unless otherwise specified by the instructor. Consider all limit states presented in this and prior chapters. Consider developing a generic spreadsheet that you can apply to similar problems.
Problems M7.1: Select the lightest section to support an axial compressive load. Analysis shows that at various times, the 15 ft long column supports 20 k Dead Load, 50 k Live Load, and 15 k Snow Load. The column is fixed at the base and is free to move and rotate at the top in all directions (think flag pole!).
Problem M7.2: A W14x90 is used a concentrically loaded column. In the plane of the web (i.e. the strong direction), the base of the column is pinned at the foundation and at the top is free to translate but not rotate. In the plane of the flanges (i.e. the weak direction), the base of the column is fixed and at the top is braced but free to rotate. The column is 25 ft long and is braced at mid height in the weak direction. Sketch both principle views of the column, complete with support conditions. Compute the axial capacity of the column. Use A588 steel.
Problem D7.1: The column located at the intersections of grids C & 6 concentrically supports 205 sqft of roof/floor space at each level. On the floor levels, 72 sqft of the supported area at each level is corridor area and the rest is dorm room area. The column also supports dead load from the roof and floors as well as snow load from the roof. Ignore area reductions allowed by the design codes. Select the lightest square HSS section to use for the column. The column is to consist of a single piece of steel that spans all three stories and is considered to be pin connected to the foundation and to the beams at each level.
The primary compression members in the tower are the legs. Bending is negligible in the legs. In the tension chapter, the braces were design based on an analysis that considers tension only in the braces. Another analysis has been run that depends on the compressive strength of the members. Note that when a brace is in compression, the intersecting brace is in tension, so the intersecting brace can be assumed to provide lateral support both in and out of plane.
For purposes of these problems, treat the ice loading as a dead load that is only present when it adds to the critical load effect.
Problem T7.1: Select a Standard Pipe Section to use for leg segment 1. Consider the foundation connection to be pinned in all directions. The leg to leg connections are considered to be moment resisting connections, creating continuity at the connection points. The braces provide lateral support for the legs where they are connected.
Problem T7.2: Redo problem T7.1 assuming that the distance between braces is double that shown on the drawings. If problem T7.1 was done, compare the results and make a few observations about effects of bracing on the design of the column legs.
Problem T7.3: Select a member for a diagonal brace at level "A". For members with bolted connections determine the required number of bolts to satisfy the limit state of bolt bearing on holes. Using the required number of bolts, neatly sketch to scale the layout out of the bolts.
There are several compression only members in this truss. The most notable is the top chord of the truss. In the plane of the truss, the members are braced against lateral movement at the joints. Out of plane the top chord is restrained laterally only at the ends of the bridge.
Problem B7.1: Select a lightest section as indicated below for diagonal member 3-7.
Problem B7.2: Double channels are to be used for the top chord of the bridge as shown in detail TBRDG 2/S3. The top plate and the lattice provide lateral support against local buckling of the built up member and are not to be considered in the area or overall moment of inertia calculation for the chord member. Assume that the distance between the backs of the channels is a clear 9 inches. Select the lightest pair of channels to use for the top chord.