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What should be the Roof slope to prevent Ponding?

As per standards, the Roof beams should have a continuous upward slope equivalent to 1/4 in/ft ( 20.8 mm/m) between a drain and the high point of a roof, in addition to minimum recommended camber to avoid ponding.

In case of insufficient slope that is less than 20.8mm/m, it should be noted that the stiffness of supporting members acting 5lb/ft2 or 239.4 N/mm2 load should not cause more than 1/2 inch or 12.7mm deflection.

What are Radial Stresses and Curvature Factor?

For a constant cross sectional the radial stress induced by a bending moment in a member is calculated by using this formula

fr=3M/2Rbd
where
M=bending moment, in lb (N m)
R = radius of curvature at centerline of member, in (mm)
b =width of cross section, in (mm)
d =depth of cross section, in (mm)

When we have a curved portion, curvature factor is introduced and is calculated as
Cc=1-2000(t/R)2

where
t is the thickness of lamination in (mm)
R is the radius of curvature of lamination in (mm).

What are the Adjustment Factors to be done in Design Values?

Their is always some variation in the design values calculated in timber. Therefore we need to apply the required adjustment to them.

Case- Extreme Fiber Bending
Fb‘=FbCDCMCtCLCFCVCfuCrCcCf

where
Fb‘ – Adjusted design value
Fb= design value for extreme fiber bending
CD= load duration factor
CM =wet service factor
CCt =temperature factor
CL =beam stability factor
CF =size factor applicable only to visually graded, sawn lumber and round timber flexural members
Cv =volume factor applicable only when beams are glued or laminated
Cfu= flat use factor applicable only to dimension- lumber beams 2 to 4 in (50.8 to 101.6 mm) thick and glued-laminated beams
Cr= repetitive-member factor—applicable only to dimension-lumber beams 2 to 4 in (50.8 to101.6 mm) thick
Cc =curvature factor—applicable only to curved portions of glued-laminated beams
Cf =form factor
When the beams are glued, laminated we have to use the smallest of the two CL or Cc

Design value for Tension
Ft‘= FtCDCMCtCF

where
Ft‘ – Adjusted design value
Ft – Design value for tension.

Adjustment For shear
Fv‘=FvCDCMCtCH

where
Fv‘ – Adjusted design value
Fv– design value for shear and CH is the shear stress factor >=1 permitted for Fvparallel to the grain for sawn lumber members.

Adjustment for compression perpendicular to the grain
design value Fc1‘is obtained from
Fc1‘=Fc1CDCtCb

where
Fc1is the design value for compression perpendicular to the grain
Cb is the bearing area factor.

Adjusted design value for compression parallel to the grain
Fc‘=FcCDCMCtCFCp
where
Fc is the design value for compression parallel to grain
Cp is the column stability factor.

Adjusted design value for end grain in bearing parallel to the grain
Fg‘= FgCDCt
where
Fg is the design value for end grain in bearing parallel to the grain.

The adjusted design value for modulus of elasticity, E’
E’= ECMCTC
where E= design value for modulus of elasticity
CT= buckling stiffness factor
C=other appropriate adjustment factors

How to Check Timber Under both Bending and Axial Load?

The members which are under the combined effect of axial as well as bending load should satisfy the following equation

Pa/P +Ma /M < 1

where
Pa total axial load on member, lb (N)
P= total allowable axial load, lb (N)
Ma= total bending moment on member, lb in (Nm)
M =total allowable bending moment, lb in (Nm)

What is the Allowable Unit Stress in Timber Columns?

Timber coloums are seldom used singly. Mostly they are a group of lumber which are stick together to form a single member. The allowable unit stress on timber is calculated by using the following formula

P/A=3.619E/(l/r)2

When the Columns have square or rectangular cross section
P/A=0.30E/(l/d)2

When the Columns have circular cross section
P/A=0.22E(l/d)2

where
P= total allowable load, lb (N)
A= area of column cross section, in2 (mm2)
c= allowable unit stress in compression parallel to grain, lb/in2 (MPa)
d= dimension of least side of column, in (mm)
l= unsupported length of column between points of lateral support, in (mm)
E= modulus of elasticity, lb/in2 (MPa)
r= least radius of gyration of column, in (mm)

Specific Conditions to be kept in mind
1) The allowable unit stress(P/A) may not exceed the allowable compressive stress c.
2) 1/d must not exceed 50.

Note: The allowable unit stresses for bearing on end grain are published by lumber associations.

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