96 4 Three-Hinged Arches
Step 2.Lay off along the vertical passing through the supportA, the value cos'k.
Step 3.Connect this ordinate with nil point. A working zone of influence line is por-
tion between sectionkand vertical passing through crownC– Right-hand
portion 1 (RHP-1). Then connect the point under crownCwith supportB
- Right-hand portion 2 (RHP-2).
Step 4. Left-hand portion (LHP) is parallel to right-hand portion 1 and connects two
points: zero ordinate at supportAand point under sectionk.
Step 5. Take into account indirect load application; connecting line between joints
2 and 3 is not shown.
Figure.4.12b presents a nonsymmetrical three-hinged arch with real nil point for
influence lineQk; this point is located within the span of the arch. Therefore, we
have one portion with positive shear and two portions with negative shear.
Location of NP.Qk/(Fig.4.12a, b) may be computed by formula
uQDltanˇ
tanˇCtan'k:4.4.3 Axial Force....................................................
Step 1.Find nil point (NP) of influence lineNk.IfloadPis located on the left half
of the arch, then reaction of the supportBpass through crownC.Axial
force at sectionkequals zero, if reaction of supportAwill be perpendicular
to tangent at pointk. The nil point./is located beyond the arch span
(Fig.4.13).
Step 2.Lay off along the vertical passing through the supportA, the value sin'k.
Step 3.Connect this ordinate with nil point and continue this line till vertical passes
through crownC. A working zone is portion between sectionkand vertical
passing through crownC(right-hand portion 1 –RHP-1). Then connect the
point under crownCwith supportB(right-hand portion 2 –RHP-2).
Step 4.Left-hand portion (LHP) is parallel to Right-hand portion 1 and connects
two points: zero ordinate at supportAand point under sectionk.
Step 5.Take into account indirect load application; connecting line between joints
2 and 3 is not shown.
Location of NP.Nk/may be computed by formulauND
ltanˇ
tanˇcot'k: