10-28-2009, 11:52 AM
Torsion always comes into play when an object is subjected to a twisting action
which may result from the fact that it has to transmit a heavy torque over a
relatively long distance.
This is as a result of an unbalanced torque or out of position moment that result from
unequal distribution of the forces along the shaft (in this case the column). This tends to
warp the object subjected to the twisting action. The force that causes this twisting
action results from the fact that the geometric centre of the structure is far from the
center of mass of the structure and it’s stiffness center; thus creating an eccentricity-
a reason for the out of balance moment.
This phenomenon could be initiated by the action of a horizontal force such as wind or
seismic load during an earthquake. If the structure is regular in both the horizontal and
vertical directions, the geometric center of the structure, center of mass and
the stiffness center of the structure coincide or are agreeably so close that the torsion
that results will be so small that it will be comfortably catered for employing the reserved
structural strength of the element in consideration-thus of no noticeable effect. But when
the condition of structural regularity is not met, the different parts of the structure will
have different geometric centers, different centers of mass and different centers of
stiffnesses, and like I mentioned before now, the whole parts of the structure will not
have a common focal or rotation point. The resultant of the these individual centers
will not be in agreement or within an acceptable range (thus eccentricity).
While the structure is not effectively restrained against rotation at the upper levels
(due to its positions in space-surrounded by air which imposes no restraint, the
structure is relatively restrained from rotation at the base due to the action of the
footing and the soil reaction. The net effect is analogues to the
twisting of a cylinder that is restrained at one end but with a couple applied at the
Other end.
The structure as a whole is rotated about its geometric center while the mass is rotated
about the center of mass. The forces and moment are distributed between the columns
in proportion to their distances from the center of mass as such the outer columns could
receive an unfairly large amount of action as compared to columns located closer to the
center of mass.
If these actions have the net effect that at any point on the top of the structure, it is loaded with
a force N (KN) which causes it to deflects by the amount ∆X(M) and ∆Y(M) in X and the
Y directions respectively and also generates a moment M(KNM) which causes a point on
the vertical member (shaft) of the frame (such as column) to rotate about the vertical
axis (the Z axis) by the amount ∆Φ, then we have the followings:-
Stiffness x = N/∆X
Stiffness y= N/∆Y
Torsional stiffness = M/∆Φ
Then torsional radius with respect to the x-axis Rx =[(M/∆Φ)/ N/∆Y]^0.5
Torsional radius with respect to the y-axis Ry = [0.5(M/∆Φ)/ N/∆X]^0.5
Both torsional radii should be ≥ 3.33 times the eccentricity for the torsional
effect not to be of any structural significance. If this condition does not hold,
(a complex situation results that sets lots of actions into play. But for simplicity
and for practical engineering concern, I would like to limit my discussion to a simplified
case that we have to consider but only the major players such as the torsion as being
discussed.) then more than proportionate twists are exacted on the furtherest columns
which when the effects are combined with those that result from the normal forces and
bending due to combined vertical and horizontal loading may exceed the load carrying
capacity of the member (such as a column) thus failure.
The twisting action that could lead to this failure could be contained by appropriate
frame layout i.e. a framing arrangement that minimizes the eccentricity. Though this is
not always a practical option but a well laid out structure in both the vertical and
horizontal directions will always help to minimize this effect. A situation will eventually
arise when the structural framing will have to be such that these complexes arise.
In such a situation, what do we do?
An indebt structural analysis has to be carried out with a keen eye kept on the
Possibility of this effect. The resultant effect of torsion is that it creates additional shear
Stresses on the member which could in combination with the normal shear stresses
test the member to beyond its structural capacity. The result from the torsion analysis
should be combined with that from the normal shear stress and the appropriate shear
reinforcement provided. Shear reinforcements in the forms of spirals or helical
arrangements should be provided as they are more effective in redistributing the
torsion stresses which tend to have circular distribution over the surface. The redistribution
of this stress will avoid local build-up of stresses at points thus, local failure which may
propagate over the whole structure-thus failure.
I hope that I am able to put my “little” idea across. Hope that the members of the engineering
community would try to make contributions so that we could have collective information
which will go a long way to enriching and or refreshing our memories.
Regards
Teddy
which may result from the fact that it has to transmit a heavy torque over a
relatively long distance.
This is as a result of an unbalanced torque or out of position moment that result from
unequal distribution of the forces along the shaft (in this case the column). This tends to
warp the object subjected to the twisting action. The force that causes this twisting
action results from the fact that the geometric centre of the structure is far from the
center of mass of the structure and it’s stiffness center; thus creating an eccentricity-
a reason for the out of balance moment.
This phenomenon could be initiated by the action of a horizontal force such as wind or
seismic load during an earthquake. If the structure is regular in both the horizontal and
vertical directions, the geometric center of the structure, center of mass and
the stiffness center of the structure coincide or are agreeably so close that the torsion
that results will be so small that it will be comfortably catered for employing the reserved
structural strength of the element in consideration-thus of no noticeable effect. But when
the condition of structural regularity is not met, the different parts of the structure will
have different geometric centers, different centers of mass and different centers of
stiffnesses, and like I mentioned before now, the whole parts of the structure will not
have a common focal or rotation point. The resultant of the these individual centers
will not be in agreement or within an acceptable range (thus eccentricity).
While the structure is not effectively restrained against rotation at the upper levels
(due to its positions in space-surrounded by air which imposes no restraint, the
structure is relatively restrained from rotation at the base due to the action of the
footing and the soil reaction. The net effect is analogues to the
twisting of a cylinder that is restrained at one end but with a couple applied at the
Other end.
The structure as a whole is rotated about its geometric center while the mass is rotated
about the center of mass. The forces and moment are distributed between the columns
in proportion to their distances from the center of mass as such the outer columns could
receive an unfairly large amount of action as compared to columns located closer to the
center of mass.
If these actions have the net effect that at any point on the top of the structure, it is loaded with
a force N (KN) which causes it to deflects by the amount ∆X(M) and ∆Y(M) in X and the
Y directions respectively and also generates a moment M(KNM) which causes a point on
the vertical member (shaft) of the frame (such as column) to rotate about the vertical
axis (the Z axis) by the amount ∆Φ, then we have the followings:-
Stiffness x = N/∆X
Stiffness y= N/∆Y
Torsional stiffness = M/∆Φ
Then torsional radius with respect to the x-axis Rx =[(M/∆Φ)/ N/∆Y]^0.5
Torsional radius with respect to the y-axis Ry = [0.5(M/∆Φ)/ N/∆X]^0.5
Both torsional radii should be ≥ 3.33 times the eccentricity for the torsional
effect not to be of any structural significance. If this condition does not hold,
(a complex situation results that sets lots of actions into play. But for simplicity
and for practical engineering concern, I would like to limit my discussion to a simplified
case that we have to consider but only the major players such as the torsion as being
discussed.) then more than proportionate twists are exacted on the furtherest columns
which when the effects are combined with those that result from the normal forces and
bending due to combined vertical and horizontal loading may exceed the load carrying
capacity of the member (such as a column) thus failure.
The twisting action that could lead to this failure could be contained by appropriate
frame layout i.e. a framing arrangement that minimizes the eccentricity. Though this is
not always a practical option but a well laid out structure in both the vertical and
horizontal directions will always help to minimize this effect. A situation will eventually
arise when the structural framing will have to be such that these complexes arise.
In such a situation, what do we do?
An indebt structural analysis has to be carried out with a keen eye kept on the
Possibility of this effect. The resultant effect of torsion is that it creates additional shear
Stresses on the member which could in combination with the normal shear stresses
test the member to beyond its structural capacity. The result from the torsion analysis
should be combined with that from the normal shear stress and the appropriate shear
reinforcement provided. Shear reinforcements in the forms of spirals or helical
arrangements should be provided as they are more effective in redistributing the
torsion stresses which tend to have circular distribution over the surface. The redistribution
of this stress will avoid local build-up of stresses at points thus, local failure which may
propagate over the whole structure-thus failure.
I hope that I am able to put my “little” idea across. Hope that the members of the engineering
community would try to make contributions so that we could have collective information
which will go a long way to enriching and or refreshing our memories.
Regards
Teddy