Building Design and Construction Handbook - Merritt - Ventech!

5.126 SECTION FIVE
72M 72M
ƒn�1 � ƒn �� (5.180)
Ah Ah
where ƒ is the stress in psi, M the moment in ft-lb from Step 4, A � plate crosssectional
area and tension is taken as positive, compression as negative.
Step 6. Apply a shear to adjoining edges to equalize the stresses there. Compute
the adjusted stresses by converging approximations, similar to moment distribution.
To do this, distribute the unbalanced stress at each edge in proportion to the reciprocals
of the areas of the plates, and use a carry-over factor of � 1 ⁄2 to distribute
the tress to a far edge. Edge 0, being a free edge, requires no distribution of the
stress there. Edge 3, because of symmetry, may be treated the same, and distribution
need be carried out only in the left half of the structure.
Step 7. Compute the midspan edge deflections. In general, the vertical component
� can be computed from
where E � modulus of elasticity, psi
k � tan � n � tan � , as in Step 3
n�1
� �
E 15 ƒn�1 � ƒn ƒn � ƒn�1
�n � � (5.181)
2 L k a a
n n n�1
The factor E/L 2 is retained for convenience; it is eliminated by dividing the simultaneous
angle equations by it. For a vertical plate, the vertical deflection is
given by
E 15(ƒn�1 � ƒ) n
�n � (5.182)
2 L hn Step 8. Compute the midspan angle change � P at each edge. This can be determined
from
E �n�1 � �n �n � �n�1
�P �� � (5.183)
2 L a a
n n�1
Step 9. To correct the edge rotations with a symmetrical loading, apply an unknown
moment of �100m n sin (�x/L), in-lb (positive when clockwise) to plate n
at edge n and �1000m n sin (�x/L) to its counterpart, plate n� at edge n�. Also,
apply �1000m n sin (�x/L) to plate (n � 1) at edge n and �1000m n sin (�x/L)
sine function is assumed to make the loading vary longitudinally in approximately
the same manner as the deflections.) At midspan, the absolute value of these moments
is 1000m n.
The 12-in-wide transverse strip at midspan, hinged at the supports, will then be
subjected at the supports to moments of 1000m n. Compute the rotations thus caused
in the slabs from