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McREL Standards Activity


CURVE COMPENSATION: HOW TO DETERMINE REQUIRED LENGTH OF CURVED LUMBER


Purpose:As a result of this activity, students will understand how to apply problem solving methods and mathematical calculations to carpentry requirements. While this activity specifies wood studs, the student will be able to apply the principles of this activity to all interior wall studs.
Related Standard & Benchmarks:
Construction
 Standard 1.Understands framing in carpentry
   Level IV [Grade 9-12]
   Benchmark 2. Knows how to frame a wall and partition, including identification of framing members; the layout locations for studs, doors, windows, and wall lines; cutting and building studs, trimmers, cripples, headers, firestops, and corners; and installation of sheathing, diagonal bracing, insulation, and a vapor barrier
Mathematics
 Standard 1.Uses a variety of strategies in the problem-solving process
   Level IV [Grade 9-12]
   Benchmark 4. Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems (i.e., uses deductive reasoning)
Mathematics
 Standard 4.Understands and applies basic and advanced properties of the concepts of measurement
   Level IV [Grade 9-12]
   Benchmark 2. Understands the concepts of absolute and relative errors in measurement
Thinking and Reasoning
 Standard 5.Applies basic trouble-shooting and problem-solving techniques
   Level IV [Grade 9-12]
   Benchmark 6. Represents a problem accurately in terms of resources, constraints, and objectives
Thinking and Reasoning
 Standard 5.Applies basic trouble-shooting and problem-solving techniques
   Level IV [Grade 9-12]
   Benchmark 10. Evaluates the feasibility of various solutions to problems; recommends and defends a solution
Construction
 Standard 1.Understands framing in carpentry
   Level IV [Grade 9-12]
   Benchmark 2. Knows how to frame a wall and partition, including identification of framing members; the layout locations for studs, doors, windows, and wall lines; cutting and building studs, trimmers, cripples, headers, firestops, and corners; and installation of sheathing, diagonal bracing, insulation, and a vapor barrier
Student Product:1.Explanation of  how you determined where and how to measure the length of stud to cut. Include all relevant details, such as:
    •Statement of goals
    •Description of means (materials and resources)
    •Explanation of problem in terms of  goals and    means
    •Explanation of possible solution(s)
    •Description of tasks involved in testing possible solution(s) including:
a. measurements (including tolerance)
b. calculations
c. diagrams/drawings
    •Description of outcome of tested solution(s)
    •Explanation of why solution(s) succeeded or failed
2.Properly cut wood stud.
Material & Resources:•Markers and chalk
•Pencils and scratch paper
•Appropriate PPE
•Wall plan
•2”x 4” framing lumber for studs and plates (top and sole)
•¼” and ½” CD plywood subfloor
•Steel tape measure
•Framing square
•Circular saw
•Exterior cord
Teacher's Note:All lumber has some degree of curving, and wood studs are no exception.  These curves can present a problem for determining the placement and size of a wall stud. Sheathing material (usually plywood and other reconstituted wood products) is fastened to the narrow side of a stud, e.g., to the 2” side of a 2x4.  There are two types of curves: a crown and a bow.  A bow curve is along the wide sides of the stud.  A crown curve is along the narrow sides, the crown being the convex, or outward, side of the curved stud.
Activity
ACTIVITY
Problem:  
Given the above materials and resources, including wood studs of differing curvature, students must determine:
1. to which side, on a 2x4 stud over 8’ in length, sheathing material should be fastened;*
2. the needed length of stud, given the following dimensions of the basic components of a wall frame:
ceiling height = 8’
sole plate = 2”
top plate = 2”
Product:
1. Explanation of  how you determined where and how to measure the length of stud to cut. Include all relevant details, such as:
•Statement of goals
•Description of means (materials and resources)
•Explanation of problem in terms of  goals and means
•Explanation of possible solution(s)
•Description of tasks involved in testing possible solution(s) including:
  a. measurements (including tolerance)
  b. calculations
  c. diagrams/drawings
•Description of outcome of tested solution(s)
•Explanation of why solution(s) succeeded or failed
2. Properly cut wood stud.

SOLUTION
1. Determining the right curve:  
Sheathing material is fastened to the narrow side of a stud, e.g., to the 2” side of a 2x4.  Since a bow curve is along the wide sides of the stud, a stud with such a curve cannot be used for a wall because the nails need to be driven along a vertically straight line, but the narrow side (which is along the face of the wall to take the sheathing) would waver right or left of that line due to the bow curve.  A  crown curve is along the narrow sides, the crown being the convex, or outward, side of the curved stud.  That side faces the wall to take the sheathing and provides a vertically straight line for the nails.
2. Where to determine the appropriate stud length:
a. Along its curve, the stud is longer than a straight vertical line from the floor to the ceiling, just as a winding road is longer than a straight road between two locations.
b. The curved stud must fit within the required vertical length of 8’, although the curve itself is greater than 8’.      
c. 8’ needs to be measured in a straight line from one point on the curve to another point.
d. Because the tape measure must be straight to take the measurement, it should be used on the     concave side of the curve, as that side would curve away from the tape, leaving an unobstructed path for measurement.  
3. Calculations to find appropriate stud length:
a.  from floor:  2’’ (sole plate)
b.  from ceiling:  2” (top plate)
c.  inches in 8’:  8 x 12” = 96”
d.  height between ceiling and sole plates for stud:  96” – 4” = 92”
e.  measure and mark  92” on stud:
    •mark one end of stud on concave side of curve
    •set tape at 8’ line to where it meets stud and  mark
4. Cut stud at marks

Wall