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Timber Design

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Submitted By noelreynapud
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Problem: Two wooden beams are to support a wooden form filled with concrete as shown. Weight of concrete is 23.5kN/m3. Neglect the weight of the wood. Span of the beam is 5m. Allowable stresses of the wood: bending = 9.72MPa, compression parallel to the grain = 8.6MPa, shear perpendicular to the grain = 2.7MPa, longitudinal shear = 0.85MPa. A. What is the depth of the two beams having a width of 50mm if bending controls? B. What is the depth of the beams having a width of 50mm if shear controls? C. What is the depth of the two beams if they would be dapped (notched) into the 150mmx150mm wooden posts as bearing areas to support the beams?
Solution:
Wt. of concrete = 0.3 x 0.9 x 23.5 kN/m3 = 6.345 kN/m
Since there are two beams the total uniform load is to be divided by two.
W= 6.345÷2; W=3.17 w = 3.17kN/m d d 5 m
Ѵmax = 7.93 kN 7.93kN 50mm
Mmax = WL28 = 9.91 kN–m
Ѵmax = 7.93kN Mmax = 9.91kN-m fb = 9.72MPa fv = 0.85MPa

A. “d “ when bending controls; fb = MyI = 6Mbd2
9.72Mpa = 6(9.91kN-m).05d2 ; d = 349.78 mm

B. “d “ when shear controls; fv = VQIb = 3V2bd
0.85MPa = 3(7.93kN)20.05d ; d = 279.88 mm C. For the dapped beam at the edge, only on shear factor can be computed for there is zero moment at the dapped (notched) area.

d’ d y

d = d’+y

For shear:

fv'd' = fvd

3V2bd'd'= fvd

3(7.93kN)2(.05)d'd'= (0.85MPa)0.34978

d’ = 312.89 mm

d = d’+y
349.78 = 312.89 + y
Y = 36.89 mm…...

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