Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
(OP)
Dear All:
Would someone please help me understand why cosine squared was used in Joseph Yura's Design Examples 1 & 2; please see the last page of the attached document.
Many thanks in advance!
jochav5280
Would someone please help me understand why cosine squared was used in Joseph Yura's Design Examples 1 & 2; please see the last page of the attached document.
Many thanks in advance!
jochav5280






RE: Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
For each inch the brace moves laterally, the brace elongates 1"/cosθ.
The horizontal component of the axial force to move the brace is F cosθ.
Stiffness is force/displacement = [F cosθ]/[1"/cosθ] = cos2θ F/displacement
RE: Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
RE: Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
RE: Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
nutte, your attachment was very helpful. I believe wannabeSE's response was incorrect now in light of nutte's attachment; what it should have said was that for every unit elongation in the brace, there is a 1/cos(theta) movement in the brace's lateral movement, (nutte had stated this in reverse order.)
Best regards,
jochav5280
RE: Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
Fhorizontal = Fbrace cosθ
Δhorizontal = Δbrace/cosθ
RE: Fundamentals of Beam Bracing: Understanding Joseph Yura's calculation of brace stiffness
Your equations were correct, however, your following post was incorrect as you can see from Yura's quote: "For each inch the brace moves laterally, the brace elongates 1"/cosθ." It should have said, for each inch the brace elongates, the brace moves laterally by 1"/cosine(theta).
Best regards,
jochav5280