CE412 Spring 2018 Lesson 17: The Force Method for Frames and Composite Structures

Lesson 17: The Force Method For Frames and Composite Structures

Wednesday, February 28, 2018

Lesson Objectives

  1. Solve 1-DOIframes using the Force Method.
  2. Solve 1-DOI composite structures that combine axial and flexural action using the Force Method.

Reading: Hibbeler (8th edition and later) - Sections10-5, 10-7; Earlier editions, see chapter 9

Homework Assignment (Due Friday)

REMINDER: The Principle of Virtual Work is one of five different methods you have for determining displacements*. While Virtual Work will often be utilized, be sure to use the easiest method (including beam formulae) to solve the unknown displacements*.

  1. King Post Beam were very common in the 19th century. The King Post Beam shown represents dimensions that would have been common, at that time, as engineers began to use timber and iron, together. The beam ABCDE is 12-feet long, made from wood (E = 1000 ksi) with a depth of 10” and a width of 4”. The vertical post CF is also wood, with a 4”x4” cross-section. The diagonal iron bars AF and EF (E=29000ksi) are ½” diameter. Assume that the beam-to-post and post-to-tie connections are pins. Do not assume that the wooden beam is axially inextensible (i.e., consider the axial virtual work in all members). Plot the moment diagram for the beam. Determine the axial forces in all members. Determine the maximum normal stress magnitude in the wooden beam and compare this with what it would have been if the underlying truss structure was not present (i.e., how much benefit was provided by “King-posting” this beam?)
  1. The structure shown is a very common style for athletic facilities (basketball courts, hockey rinks, etc). It consists of a rigid frame, supported by the pin-roller foundations shown, but an “underslab” tension-tie (typically, a cluster of rebar, encased in concrete) turns the structure into 1-DOI. If the frame is made from W24x84 steel shapes (in strong-axis bending) and the underslab tension-tie consists of 6 number 5 steel rebars (total tension area of 1.84 in2), determine the force in the tie and plot the moment diagram of the frame. Assume the materials remain elastic.
  1. Determine the support reactions and plot the moment diagram.

Given: A beam carrying a uniformly-distributed load of 1 kip/ft over a span of 30 feet is supported by pins at A and C and asoil spring at C, with a spring constant kC = 5 kip/ft. EI=1000kip-ft2