Download The Method of Sections: Determining Forces in Truss Members and more Study Guides, Projects, Research Engineering in PDF only on Docsity! Lecture 20 ENGR-1100 Introduction to Engineering Analysis THE METHOD OF SECTIONS In-Class Activities: โข Reading Quiz โข Applications โข Method of Sections โข Concept Quiz โข Group Problem Solving โข Attention Quiz Todayโs Objectives: Students will be able to determine: 1. Forces in truss members using the method of sections. STEPS FOR ANALYSIS 1. Decide how you need to โcutโ the truss. This is based on: a) where you need to determine forces, and, b) where the total number of unknowns does not exceed three (in general). 2. Decide which side of the cut truss will be easier to work with (minimize the number of external reactions). 3. If required, determine any necessary support reactions by drawing the FBD of the entire truss and applying the E-of-E. STEPS FOR ANALYSIS (continued) 4. Draw the FBD of the selected part of the cut truss. You need to indicate the unknown forces at the cut members. Initially, you may assume all the members are in tension, as done when using the method of joints. Upon solving, if the answer is positive, the member is in tension as per the assumption. If the answer is negative, the member must be in compression. (Please note that you can also assume forces to be either tension or compression by inspection as was done in the figures above.) 5. Apply the scalar equations of equilibrium (E-of-E) to the selected cut section of the truss to solve for the unknown member forces. Please note, in most cases it is possible to write one equation to solve for one unknown directly. So look for it and take advantage of such a shortcut! STEPS FOR ANALYSIS (continued) EXAMPLE (continued) Now use the x and y-directions equations of equilibrium. โ + ๏ FY = 56.7 โ 20 โ 30 โ (4/5) FKD = 0; FKD = 8.38 kN (T) โ + ๏ FX = (โ 75.1) + (3/5) ( 8.38 ) + FCD = 0; FCD = 70.1 kN (T) 56.7 kN READING QUIZ 1. In the method of sections, generally a โcutโ passes through no more than _____ members in which the forces are unknown. A) 1 B) 2 C) 3 D) 4 2. If a simple truss member carries a tensile force of T along its length, then the internal force in the member is ______ . A) Tensile with magnitude of T/2 B) Compressive with magnitude of T/2 C) Compressive with magnitude of T D) Tensile with magnitude of T CONCEPT QUIZ 1. Can you determine the force in member ED by making the cut at section a-a? Explain your answer. A) No, there are 4 unknowns. B) Yes, using ๏ MD = 0 . C) Yes, using ๏ ME = 0 . D) Yes, using ๏ MB = 0 . ATTENTION QUIZ 2. When determining the force in member HG in the previous question, which one equation of equilibrium is the best one to use? A) ๏ MH = 0 B) ๏ MG = 0 C) ๏ MB = 0 D) ๏ MC = 0 GROUP PROBLEM SOLVING a) Take the cut through members GF, GB and AB. b) Analyze the left section. Determine the support reactions at A. Why? c) Draw the FBD of the left section. d) Apply the equations of equilibrium (if possible, try to do it so that every equation yields an answer to one unknown. Given: Loads as shown on the truss. Find: The force in members GB and GF. Plan: GROUP PROBLEM SOLVING (continued) 1) Determine the support reactions at A by drawing the FBD of the entire truss. +โ ๏ FX = AX = 0 + ๏ MD = โ AY (28) + 600 (18) + 800 (10) = 0; AY = 671.4 lb Why is Ax equal zero by inspection?
