MEP-Technical Manual CDN 0408.qxd - Hambro

DESIGN PRINCIPLES AND CALCULATIONS
For a uniformly loaded joist, the average interface shear s,
at ultimate load when calculated by ultimate strength
principles, would be:
s = 2T u
L
......................................................... (B)
and would represent the average shear force, per unit
length, between the points of zero and maximum moment.
Some modification to this formula would occur when the
strain neutral axis at failure would be located within
the section. As this modification is slight and would only
occur with bottom chord areas greater that 1 185 mm 2 ,
it is neglected.
The following compares the elastic and ultimate approaches:
Since M u = T u d u equation (B) can be rewritten:
s = 2M u
d u L
......................................................... (C)
Also, for a uniformly distributed load,
Mu =
......................................................... (D)
VuL 4
Subscipts u, are added to equation (A) to represent the
arbitrary “q” force at failure:
q u = V u Q
I c
Combining (C) and (E) results in:
q u = d u L x V u Q
s
2M u
......................................................... (E)
and, substituting (D) into equation (F),
q u = 2Qd u
s
I c
I c
.............................................. (F)
...................................................... (G)
The value I c /Qd u has been calculated for the various
Hambro composite joist sizes. It is constant, and = 1.1.
Substituting this in (G), gives:
qu = 1.82
s
This verifies that q and s are closely related and that the
interface shear force does, in fact, vary from a maximum at
zero moment (maximum vertical shear) to a minimum at
maximum moment (zero vertical shear).
The more recent full testing programs have consistently
established a failure value for the horizontal bearing forces
and the friction between steel and concrete. An additional
contributing factor is a hole in the section at each 178 mm
on the length.
(i) Horizontal bearing forces
The test has defined an ultimate value for the
end bearing shoe Bu = 222 kN for a concrete
strength = 20 MPa
(ii) Friction between steel and top chord
The failure value for the interface shear
qu = 36.9 N/mm. This is sometimes converted
to “bond stress” u = q / embedded S perimeter
= q /178 mm. Hence, the ultimate “bond stress”
u = 36.9 / 178 = 207 kPa.
The safety limiting interface shear is defined by
using a safety factor of 2 on point (i) and (ii).
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