Question

Determine if a 15-ft long 6x14 beam is adequate to support a dead load wD= 0.16 kip/ft and a live load wL= 0.25 kip/ft. The member is unincised-Select Structural Eastern Hemlock with MC > 19% and a normal temperature range. Live load deflection should not exceed L/360 and total deflection should not exceed L/240. The member is part of a floor system and is repeated every 26-in. It is also fully braced by the floor sheathing and sits on a 4-in wide beam (nominal) on each side. Make sure you check all limit states even if the first one you check shows the beam to be inadequate.

Answer 1

Given:

L=15 ft

Beam size=6 x 14

W _D=0.16 kip/ft

W _L=0.25 kip/ft

Step 1:

W_u=1.2(D.L)+1.6(L.L)

W_u=1.2(0.16)+1.6(0.25)

W_u=0.592 kip/ft

M=W_uL² / 8

M=(0.592 x 15²) /8

M=16.65 kip-ft

Step 2: Check the value of bending stress

f_b=M/S_x

f_b=16.65 x 1000 x 12/(167.06)

f_b=1196.7 psi

F_b=1000 psi (Not safe)

Step 3:

Shear=0.592 x 15 /2=4.44 kips

Maximum shear stress=1.5(V)/A

Maximum shear stress=1.5 x 4.44/(74.25)

Maximum shear stress=89.7 psi

Permissible shear=150 psi (safe)

Step 4:

Deflection:

=5wL⁴/(384EI)

=5x(0.16/12)x(15x12)⁴/(384x29000x1127.67)

=0.0055 in

permissible=L/360=15x12/360=0.5 in

Total deflection:

=5x0.42/12x(180)⁴/(384x29000x1127.67)

=0.014 in

permissible=L/240=15x12/240=0.75 in

The beam is not adequate at it has failed in bending stress, so it cannot be used, to use the beam we need to increase the size of the beam