Discussion

[chigozie]

I think that it will be a wise thing to do if we could pick up (at intervals) any topic that is of engineering interest as to discuss it. In this way (I believe), we could learn from one another and also refresh our memories on the areas of engineering that we do not have time to read up to.
I think that this will also serve as an on-the-site continuous education program. What do you think about it?
Regards
Teddy

[concreteok]

I always like this idea. To share the 'experts' view. But how do u suggest we start with?

[chigozie]

I feel (my opinion) we could start by:-
You (I mean anyone that has an interest) can suggest a topic that you think could be of interest or a topic that you feel is less discussed, or that which you do not understand very well etc. By so doing, this could set up a platform for everyone to make his or her own contribution. (Two good engineering heads are better than one).
Regards
Teddy

[RedHorse]

may i suggest we start with building "horizontal torsion"

[chigozie]

Interesting!!
I have not heard of something like that for a time-while. What does it talk about?
Teddy

[RedHorse]

Building Horizontal Torsion. Irregularly shaped buildings tend to twist during seismic loading causing the exterior columns to be subjected to additional torsional moments, thus causing the structure to fail. Nearly all 3D finite element analysis software accounts for all deflections including building twisting but most column design does not consider column torsion. I humbly ask my fellow structural engineers to shed light on the matter.

[chigozie]

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

[pisano]

A realy academical discussion. Grazie Teddy !

[chigozie]

It is about 3 weeks today that I wrote the last contribution to the topic (referred to) and till this moment, there has not been any further contribution to the said issue.
I believe we are all awake !!
Please gents, Lets keep it moving. We cannot afford to remain in the same position for eternity. Lets get it on, lets keep it on, lets get moving
Regards
Teddy

[chigozie]

In my penultimate post (post #7), I hinted that one of the best options for the column section is a circular one.
Why? -
This is due to the fact that torsion tends to assume a concentric form or radiates from a common center as such the most convenient form to suit its distribution is that of a circle represented as a circular cross section.
· The direction of the horizontal load is unpredictable as such a structural form that has an indefinite numbers of edges as represented by a circular cross section is the most ideal to counter its effect.
· The seismic load is assumed to occur in 2-orthogonal directions. This direction is not defined as such it could be at any of the infinite combinations of points in space. The best structural form that could adjust to any of the directions that this load could decide to occur is that of a circular cross section (since it has an indefinite number of edges as such could accommodate the force equally, no matter the direction of its application).
· Cylindrical members tend to have uniform structural strength distribution (homogeneity) due to the fact that it does not have blind spots (unlike other structural forms such as the polygons that tend to have blind spots due to their edges as such the strength distribution is most none uniform as concrete tend to segregate around the edges-thus lose their consistency/strength).
Consider the equation of the stress on a structural member:
= p/A MY/I. This implies that the stress experienced diminishes with increased moment of inerter. So for cross sections of the same cross sectional area, the difference could only be made by the difference in the moment of inerter (I) and Y which is the distance of the most stressed fiber from the neutral axis of the member. If we combine Y/I, we have 1/Z, where Z is the section modulus, as such the difference could only be made by the section modulus of the individual cross sections chosen. Let’s compare the section modulus of some common structural cross sections (the rectangle, square and circular cross sections) of the same cross sectional area 300mm x 450mm in torsion: -
For gravitational loads only (in this case the direction of application of the load is defined), the square, then the rectangular sections are surely the ideal ones as there is no doubt that they have greater section module when compared to the circular one (i.e. d^3/3 (= 1.65x10^7mm^3) for the square section , bd^2/6 = 300x450^2/6 (= 1.0x10^7mm^3) for the rectangular section and PiR^3/4 (= 7.0x10^6 mm^3)for the circular section). But if the direction of the application of the load is not known, then we have to consider all possible critical directions, including: -

Rectangle:-
Area: - 135000 mm^2
Dimension: - 300mm x 450mm
Z: - bd^2/6 = 450x300^2/6 (=6.75 x 10^6)
Square:-
Area: - 135000 mm^2
Dimension: 367.42mm x 367.42mm
Z: - d^3/3 ( =1.65x10^7)
Circular:-
Area: - 135000 mm^2
Dimension: - R = 207.3mm
Z: - PiR^3/4(=7.0x10^6)


When oriented such that the axis of bending passes through the diagonal of the structural element, we have:-
Rectangle:-
Area :- 135000 mm^2
Dimensione:- 300mm x 450mm
Z :- b^2d^2/6 SQR(d^2 + b^2)
= 300^2x450^2/3245
= 5.61x10^6
square:-
Area :- 135000 mm^2
Dimensione:- 367.42mm x 367.42mm
Z :- d^3/6SQR2 = = 0.117x367.42^3 = =5.84X10^6
Circular:-
Area :- 135000 mm^2
Dimensione:- R = 207.3mm
Z :- Pi R^3/4 = = 7.0x10^6
Since design is usually made considering the most critical condition, it implies that we have to use the least section modulus in our design (which will give the highest stress) i.e.:-
Rectangle:-
5.61x10^6mm^3
square:-
5.84X10^6mm^3
circular:-
7.0x10^6 mm^3
The above results give us the ratio of 1 : 1.04 : 1.25
Note that, apart from the fact that the circular section provided the greatest modulus of elasticity as such experienced the least stress, also in all the possible situations(i.e. no matter the direction of application of the load), section modulus for the circular section remained same while it varied for all other sections considered. This implies that circular cross section is more reliable as a structural section for column design in situations in which the actual direction of application of the load could not be predicted as is the case in which torsion is to play a considerable part (we can not predict with certainity, the angle of attach of wind load and earthquake).
Regards
Teddy