In the shape cal cu la tor, you may spec ify the num ber of seg ments into which the ca ble ob ject should be bro ken. Each seg ment will be mod eled as a sin gle cat e nary ca -ble or sin gle frame el e ment.
For the cat e nary el e ment, a sin gle seg ment is usu ally the best choice unless you are con sid er ing con cen trated loads or in ter me di ate masses for ca ble vi bra tion.
For the frame el e ment, mul ti ple seg ments (usually at least eight, and some times many more) are re quired to cap ture the shape vari a tion, un less you are mod el ing a straight stay or brace, in which case a sin gle seg ment may suf fice.
For more in for ma tion, see Chap ter “Ob jects and Elements” (page 7)
Degrees of Freedom
The Ca ble el e ment ac ti vates the three translational de grees of free dom at each of its con nected joints. Ro ta tional de grees of free dom are not ac ti vated. This el e ment con trib utes stiff ness to all of these translational de grees of free dom.
For more in for ma tion, see Topic “De grees of Free dom” (page 30) in Chap ter
“Joints and De grees of Free dom.”
Local Coordinate System
Each Ca ble el e ment has its own el e ment lo cal co or di nate sys tem which can be used to de fine loads act ing on the el e ment. The axes of this lo cal sys tem are de noted 1, 2 and 3. The first axis is di rected along the chord con nect ing the two joints of the el e ment; the re main ing two axes lie in the plane per pen dic u lar to the chord with an ori en ta tion that you spec ify. This co or di nate sys tem does not nec es sar ily cor re
-150 Degrees of Freedom
spond to the di rec tion of sag of the ca ble, and does not change as the di rec tion of sag changes dur ing load ing.
The def i ni tion of the ca ble el e ment lo cal co or di nate sys tem is not usu ally im por tant un less you want to ap ply con cen trated or dis trib uted span loads in the el e ment lo cal sys tem.
The def i ni tion of the Ca ble lo cal co or di nate sys tem is ex actly the same as for the Frame el e ment. For more in for ma tion, see Topics “Lo cal Co or di nate Sys tem”
(page 93) and “Ad vanced Lo cal Co or di nate Sys tem” (page 95) in Chap ter “The Frame El e ment.”
Section Properties
A Cable Sec tion is a set of ma te rial and geo met ric prop er ties that de scribe the cross-sec tion of one or more Ca ble el e ments. Sec tions are de fined in de pend ently of the Ca ble el e ments, and are as signed to the el e ments.
Ca ble Sec tions are al ways as sumed to be cir cu lar. You may spec ify either the di am -e t-er or th-e cross-s-ec tional ar-ea, from which th-e oth-er valu-e is com put-ed. B-end ing mo ments of in er tia, the tor sional con stant, and shear ar eas are also com puted by the pro gram for a cir cu lar shape.
Material Properties
The ma te rial prop er ties for the Sec tion are spec i fied by ref er ence to a pre vi -ously-de fined Ma te rial. Iso tro pic ma te rial prop er ties are used, even if the Ma te rial se lected was de fined as orthotropic or anisotropic. The ma te rial prop er ties used by the Sec tion are:
• The modulus of elas tic ity, e1, for ax ial stiff ness
• The co ef fi cient of ther mal ex pan sion, a1, for tem per a ture loading
• The mass den sity, m, for com put ing el e ment mass
• The weight den sity, w, for com put ing Self-Weight and Grav ity Loads
The ma te rial prop er ties e1 and a1 are ob tained at the ma te rial tem per a ture of each in di vid ual Ca ble el e ment, and hence may not be unique for a given Sec tion. See Chap ter “Ma te rial Prop er ties” (page 69) for more in for ma tion.
Section Properties 151
Geometric Properties and Section Stiffnesses
For the cat e nary for mu la tion, the sec tion has only ax ial stiff ness, given by a e1× , where a is the cross-sec tional area and e1 is the modulus of elas tic ity.
Mass
In a dy namic anal y sis, the mass of the struc ture is used to com pute in er tial forces.
The mass con trib uted by the Ca ble el e ment is lumped at the joints I and j. No in er -tial ef fects are con sid ered within the el e ment it self.
The to tal mass of the el e ment is equal to the undeformed length of the el e ment mul -ti plied by the mass den sity, m, and by the cross-sec -tional area, a. It is ap por -tioned equally to the two joints. The mass is ap plied to each of the three translational de -grees of free dom: UX, UY, and UZ.
To cap ture dy namics of a ca ble it self, it is nec es sary to di vide the ca ble ob ject into mul ti ple seg ments. A minimum of four seg ments is rec om mended for this pur pose.
For many struc tures, ca ble vi bra tion is not im por tant, and no sub di vi sion is nec es -sary.
For more in for ma tion:
• See Topic “Mass Den sity” (page 77) in Chap ter “Ma te rial Prop er ties.”
• See Topic “Sec tion Prop er ties” (page 151) in this Chap ter for the def i ni tion of a.
• See Chap ter “Static and Dy namic Anal y sis” (page 307).
Self-Weight Load
SelfWeight Load ac ti vates the selfweight of all el e ments in the model. For a Ca -ble el e ment, the self-weight is a force that is dis trib uted along the arc length of the el e ment. The mag ni tude of the selfweight is equal to the weight den sity, w, mul ti plied by the crosssec tional area, a. As the ca ble stretches, the mag ni tude is cor re -spond ingly re duced, so that the to tal load does not change.
Self-Weight Load al ways acts down ward, in the global –Z di rec tion. You may scale the self-weight by a sin gle scale fac tor that ap plies equally to all el e ments in the struc ture.
152 Mass
For more in for ma tion:
• See Topic “Weight Den sity” (page 78) in Chap ter “Ma te rial Prop er ties” for the def i ni tion of w.
• See Topic “Sec tion Prop er ties” (page 151) in this Chap ter for the def i ni tion of a.
• See Topic “Self-Weight Load” (page 295) in Chap ter “Load Pat terns.”
Gravity Load
Grav ity Load can be ap plied to each Ca ble el e ment to ac ti vate the self-weight of the el e ment. Us ing Grav ity Load, the selfweight can be scaled and ap plied in any di -rec tion. Dif fer ent scale fac tors and di -rec tions can be ap plied to each el e ment. The mag ni tude of a unit grav ity load is equal to the weight den sity, w, mul ti plied by the crosssec tional area, a. As the ca ble stretches, the mag ni tude is cor re spond ingly re -duced, so that the to tal load does not change.
If all el e ments are to be loaded equally and in the down ward di rec tion, it is more con ve nient to use Self-Weight Load.
For more in for ma tion:
• See Topic “Self-Weight Load” (page 118) in this Chap ter for the def i ni tion of self-weight for the Frame el e ment.
• See Topic “Grav ity Load” (page 296) in Chap ter “Load Pat terns.”
Distributed Span Load
The Dis trib uted Span Load is used to ap ply dis trib uted forces on Ca ble el e ments.
The load in ten sity may be specified as uni form or trap e zoidal. How ever, the load is ac tu ally ap plied as a uni form load per unit of undeformed length of the ca ble.
The to tal load is cal cu lated and di vided by the undeformed length to de ter mine the mag ni tude of load to ap ply. As the ca ble stretches, the mag ni tude is cor re spond -ingly re duced, so that the to tal load does not change.
The di rec tion of load ing may be spec i fied in a fixed co or di nate sys tem (global or al ter nate co or di nates) or in the el e ment lo cal co or di nate sys tem.
Gravity Load 153
To model the ef fect of a non-uni form dis trib uted load on a cat e nary ca ble ob ject, spec ify mul ti ple seg ments for the sin gle ca ble ob ject. The dis trib uted load on the ob ject will be ap plied as piecewise uni form loads over the seg ments.
For more in for ma tion:
• See Topic “Dis trib uted Span Load” (page 121) in Chap ter “The Frame El e -ment.”
• See Chap ter “Ob jects and Elements” (page 7) for how a sin gle ca ble ob ject is meshed into el e ments (seg ments) at anal y sis time.
• See Chap ter “Load Pat terns” (page 291).
Temperature Load
Tem per a ture Load cre ates ax ial ther mal strain in the Ca ble el e ment. This strain is given by the prod uct of the Ma te rial co ef fi cient of ther mal ex pan sion and the tem -per a ture change of the el e ment. All spec i fied Tem -per a ture Loads rep re sent a change in tem per a ture from the un stressed state for a lin ear anal y sis, or from the pre vi ous tem per a ture in a non lin ear anal y sis.
The Load Tem per a ture may be con stant along the el e ment length or in ter po lated from val ues given at the joints.
See Chap ter “Load Pat terns” (page 291) for more in for ma tion.