Deflection and Camber
General Discussion | Example
General Discussion
- The governing equation for deflection is Dmax £
Dall.
- Dall criteria:
- Dall criteria are often given in terms of the member's span, L, in inches.
- '94 UBC 1608, Table 16-D for roof members supporting plaster ceilings and
for floor members.
- Dall = L/360
- where Dmax is calculated for live load only.
- a user comfort criteria.
- Dall = L/240
- where Dmax is calculated for a total load of live + (k)dead.
- with k=1.0 for unseasoned lumber and .5 for seasoned lumber (MC £ 19%).
- criteria attends to member creep and unpleasant visual cracking of ceiling.
- UBC criteria is very limited.
- Dall = L/360
- Additional D guidelines provided by AITC as shown in figure 2.8 of Breyer
(p. 32). Examples include:
- Industrial roof beams: DLL £ L/180.
- Floor beams with increased stiffness: DLL £ L/480
- AITC recommends a minimum roof slope of 1/4"/ft for all roof members to prevent ponding.
- Rule of thumb: any roof member should be stiff enough so that a 5 psf uniform load results in D £ 1/2" to minimize ponding potential.
- Dmax = f(P, w, and L/IE') where E' = E CM Ct CT.
- E = tabulated modulus of elasticity about the axis of bending - given as an average value.
- CT = buckling stiffness factor used primarily in column calculations and therefore takes a value of 1 for beams.
- Note: CD does not apply to E.
- Camber = initial curvature built into member to oppose the deflection of the beam under gravity loads.
- Typical glumlam camber = 1.5DD.
- Produces a nearly level beam under long term deflection.
- Creep = the time dependent deformation that develops at a slow, but steady rate over long periods of time.
- Creep is greater for wood members drying under load or exposed to varying temperature and humidity conditions.
- To estimate the long term deflection accounting for creep, increase the long term load component by 1.5:
Example:
- This example problem has been adapted and modified from Structural Design in Wood by J. Stalnaker and E. Harris.
- Determine the short and long term flexural deflection and compare against the '94 UBC criteria.
