From: "Joseph M. Otto, P.E." <jmo_engineering(--nospam--at)email.msn.com>
Date: Mon, 14 Feb 2000 13:12:44 -0800
This is not necessarily a shear flow question. If there were two beams side
by side made of the same material of equal cross section which were
uniformly and equally loaded, there wouldn't be any shear between them and
they would deflect the same amount.
Keep in mind though that the analysis for reinforcing an existing member
that is in service is very different than one for reinforcing a member
before it is put into service.
If a simple span GLB is a part of an existing structure and new channels are
bolted to the GLB at the neutral axis, it seems to me that the only force
transferred through the bolts into the channels is that which is caused by
live loading when the composite section is loaded and deflects. The amount
of live load to each member can be proportioned according to the percentages
of the composite moment of inertia. A transformed section should be used
when calculating the moment of inertia of the GLB. The GLB will take all of
the dead load + ((Transformed I / Composite I)* Live Load). The channels
will take a percentage of the live load dependant on their moment of
inertia's divided by the composite moment of inertia. The end reactions of
the new channels will have to be accounted for.
The analysis is similar if it is new construction except that the force
transferred through the bolts is from dead + live loads.
Joe Otto, P.E.
From: Gobo, Gina [mailto:ggobo(--nospam--at)DLRGROUP.com]
Sent: Monday, February 14, 2000 11:43 AM
Subject: Shear Flow
I have question about composite beams:
I have a wood glulam beam that I would like to reinforce by adding a steel
channel to both sides. I am trying to find the shear flow at the channel to
wd beam contact area so that I may figure our how many bolts I need to
faster the composite beam together. I am using the formula f = QV/I, where V
is the maximum shear load on the beam, I is the moment of inertia for the
composite section, and Q the first moment of inertia of the glulam beam that
is in contact with the channel = yA where, y is the distance from the
centroid of the block of wd in contact with the channels to the neutral axis
and A is the area of the same block of wd. If I am using a channel that is a
C12X20.7 and a 6.75X31.5 glulam, Q = ((12/2)-dist to neutral axis of entire
section)*6.75*12=248in3. I = 17964.83 in4 and V = 48kips. f = 8kip/ft which
seems very high.
The shear flow that I get seems very high. Do I have to use the transformed
section in order to get the shear flow? (i.e. transform the wd beam into an
equivalent steel member in order to get the correct shear flow). Or, is
using I of the composite section based on the geometry of the cross section
Gina T. Gobo, E.I.T.