Unformatted text preview: Appendix A
Frame Analysis Program
A1. How to Run the Program Frame.Cmp
5. Run CMAP
Open the program Frame.Cmp found in CMAP-directory
Execute the program.
Select Data-menu to start the process of data input /editing.
Select Plot-Moments-menu to plot the bending moment diagram. A2. Modeling and Data Input for an Example System
1. Fundamental of modeling
1. A frame system is an assembly of nodes and members. A member is
defined by a line connecting two nodes. Thus, the nodes serve to connect
the members together as well as to connect the members to the supports.
2. In general, a node may translate in x- and y-directions as well as to
rotate. Each free displacement will generate a nodal equilibrium equation
expressing the balance between external forces and resisting member
forces acting on the node.
3. A member-end that is fixed to the node will provide moment resistance to
the node (unless its moment of inertia is negligible). Thus, a moment
connection between members is modeled by fixing the ends of the
members to the common node.
4. For modeling pinned and mixed connections, a member-end may be
pinned to the node, and thus it will not provide any moment resistance to
The above principles are used in modeling the example frame (Fig.A1) as
shown in Fig.A2. Followings are some explanations of the model.
o Appendix A Since members 2 and 3 are fix-fix type (see Note 1 below), the pinned
connection at c must be modeled by a pair of coupled nodes (2 & 3).
These nodes share the same x- and y-translations, but they have A.1 independent rotations (i.e. the nodes are coupled in translations but uncoupled in rotations as required by the pinned connection). This couplednode model has the advantage that the computed result will include the
rotations of both nodes. Note that alternate models for pinnedconnections exist as shown in Fig.A3(b). 40 kN
I = 554×106 mm4
a 10 kN/m 20 kN.m
c b Girdir abcd:
• negligible axial deformations
• I = 554×106 mm4
Supporting members fb and fd:
• Pinned at both ends
• A = 10800 mm2 e d 8m
A = 10800 mm2 f
12m 10 kN.m E = 200 GPa all members 6m 6m 12m Figure A1: Example System y Nodes coupled in translations Node numbers Member axes ij 6 8
1 1 2 2 3 4 5 4 6 6 5
nodal translations 3 Member
nodal rotation Figure A2: A Model for Analysis of the Example System
o o Members 5 and 6 are pin-connected to the nodes at both ends. They are
pin-pin members (type 3). o Appendix A Members 1, 2, 3 and 4 have their ends rigidly fixed to the nodes. They are
fix-fix members (type 0. See Note 1 below). The restrained translations at nodes 1, 6 and 7 are as required by the
support conditions. A.2 o The rotation of node 7 is artificially restrained because the pin-pin
members 5 & 6 provide NO rotational resistance to the node 7. This
rotational restraint is necessary in order to stabilize node 7. Data input for this model and are described below. Any consistent set of units
(e.g. meters and kN) may be used. This Sample Data can be invoked within
the Frame.Cmp program by the menu SampleData.
General Sub-menu items
• Elastic modulus
• No. of elements
• No. of nodes
• No. of restrained
nodes Data input
Example frame in Fig.A1
Max 255 characters
An Element is a member
Nodes 1, 6 and 7 where nodal
displacements are to be specified (e.g.
For book-keeping only 3 • No. of loading cases
• No. of pairs of
(How members are
connected together) MemberProperties SupportRestraints Loading Appendix A • Area • Inertia Geometry 1
0, 12, 18, 18, 24, 36, 18
0, 0, 0, 0, 0, 0, -8
1, 2, 0
2, 3, 0
4, 5, 0
5, 6, 0
7, 2, 3
7, 5, 3
0, 0, 0, 0, 10800e-6, 10800e-6 554e-6, 554e-6, 554e-6, 554e-6, 0, 0 • Support conditions 1,
7, R, R, F
R, R, F
R, R, R • Coupled nodes
• Load case No.
• No. of loaded
nodes(See Note 3) 3,
1 4, 2 1, 1, 0 1 pair (Nodes 2 and 3 are coupled in
x- & y-translations).
x-coordinates (m) of nodes 1, 2, .... 7
y-coordinates of nodes
One row per member:
Col.1: Node i
Col. 2: Node j
Col. 3. End fixity to nodes (See Note
• Pin-pin (type 3)
Cross-sectional areas in m2. (Zero is
used if axial deformation in a member
is neglected. This zero will be
automatically replaced by a suitably
Moments of inertia in m4. Inertias for
pin-pin members are not used in the
See Note 2(a) below.
One row per node. See Note 2(b). One row per pair.
For book-keeping only
Two nodes (3 and 6) have external
forces. A.3 • No. of element loads
(see Note 4).
• Nodal load data
(See Note 3)
• Element load data
(see Note 4). One element load on member 4 .
0, • Forces on node 3
• Forces on node 6
Uniform load on member 4. 12 Note 1. Member Fixity code: array ElCon
Each member will have its own local member axes defined by the nodes i
and j (see Fig. A4) of the two end. When two members share the same
node, they are connected via this common node. If the member-ends are
(fully) fixed to the common node (Fig. A3a), they also share the node's
translations and rotation (i.e. a moment or rigid connection).
To model a pinned connection (Fig.A3b), we must uncouple the rotation of
the pinned-end from that of the other members (e.g. by pinning the
member-end to the node or by using coupled node as shown in the example
problem). This feature leads to different member types. Member ends
fixed to node Member ends
fixed to node (a) Moment connection A
B Member end
pinned to node (b) Member AB pinned to node A Figure A3
The last column of the array ElCon (ElementConnectivity) contains the Fixity
code which specifies the type of member-end fixty conditions as follows:
3: Fix-fix member type (both ends are fixed to the nodes)
Pin-fix member type (end i is pinned to the node)
Fix-pin member type (end j is pinned to the node)
Pin-pin member type (both ends pinned to the nodes) Note 2: Support Conditions and Coupled Nodes
a) Support Conditions: array aSNode Appendix A A.4 Every node in the system has three free nodal directions unless support
condition is given to restrain the individual directions. This support restraint
data is defined via the array aSNode (array of SupportedNodes) as follows:
Column 1: Enter the node-number where one or more directions are to
Column 2: If x-direction is restrained, otherwise enter F for free
Column 3: If y-direction is restrained, enter R, otherwise enter F for
Column 4: If rotation is restrained, enter R, otherwise enter F for free
b) Coupled nodes: array aCNode
When two nodes j and k have equal translation(s) and/or rotation, the
nodes are said to be a coupled pair. The data for a coupled pair are specified
in the following sequence:
Node j Node k 1 if coupled in x-displ,
zero otherwise 1 if coupled in y-displ,
zero otherwise 1 if coupled in rotation, zero
otherwise Note 3: Nodal Loads: array aNLoad
All forces acting on a node are specified in one row of array aNLoad:
Node No. Force in x-direction Force in y-direction Moment Note 4: Member (Element) Loading: array aELoad
Data for each member (Element) load are specified in one row of array
aELoad. If a member is subject to 3 different member loads, this will count as
3 Element Loads.
No. Load type 1 or
2 or 3
(Fig. A4) Fx (Type 1)
(Type 3) Fy (Type 1)
or Tb (Type 3) a (Type 1)
(Type 3) Three types of member load are available in the program:
Type 1: concentrated force as specified by: Fx, Fy and a (Fig.A4a).
Type 2: uniform load as specified by: w, a and b (Fig.A4b).
Type 3: temperature as specified by: Tt, Tb and D (Fig.A4c).
Note that external member forces are positive in the positive directions of the
member's local axis-system. The member's x-axis goes from node i to node Appendix A A.5 j, and the member's y-axis is 90o counterclockwise from the x-axis.
Distances a and b are measured from the end i of the member. Fy
y x i Fx Tt j j
w y y
a i (a) Type 1 x
b (b) Type 2 Tb D j i (c) Type 3: Temperatures Figure A4: Sign conventions for positive member loading A3. Analysis and Results
Once the data have been input/edited and verified, computation is initiated
by selecting one of the following item in the main menu panel:
• ANALYSE to do only the analysis and the results will be placed in the output
• PLOT DEFORMED SHAPE: To analyse as well as to plot the deformed shape.
• PLOT MOMENT DIAGRAM: To analyse as well as to plot the moment
diagram. The deformed shape may also be plotted here: (i) First, set a
different color by pressing key 'C' and (ii) Press key 'D'.
Errors in data input can often be detected by inspection of the plotted
deformed shape and moment diagram. Data can be revised/edited by
selecting the DATA menu again.
Interpretation of the output for member forces
Six member-end forces are displayed in the output document. They are given
both in local member axes and global (system) axes. The order are always as
5: Appendix A x-Force on end i
y-Force on end i
Moment on end i
x-Force on end j
y-Force on end j (local member x-axis or global x-axis)
(local member y-axis or global y-axis)
(local member x-axis or global x-axis)
(local member y-axis or global y-axis) A.6 6: Moment on end j
Print or Save the Output Document
First you must quit the Frame.Cmp program, and then use the main CMAP
Additional Features in Frame.Cmp
There are many other features in the Frame.Cmp program. These are easily
discovered merely by trying them using the displayed menus. A4. Additional Example Frames
Additional sample data files (Frame1.dat, Frame2.dat, Frame3a.dat,
Frame3b.dat, Frame4.dat) are available in the compressed file
SampleData.zip. The geometry and loading for the frames are as shown in
30 kN/m 50 kN 10 kN/m 60 kN
a a 1 b 12 kN.m 2 2m d c b c 3m 6m 3 I = 52.9×106mm 4 f e d [email protected]=6m 4.8 m 3m 4.8 m 4.8 m Frame 1 Frame 2
10kN/m 40 kN
a 1 b 10 kN/m 2 3
6 5 d 4 f
12m 6m 6m 12m Frames 3a, 3b a
8m E = 200 GPa Cable
A = 314mm2 f e
2m d c b 2m 2m Beam and posts: I = 10.91×106mm 4 Frame 4 Figure A5: Geometry and loading of sample frames Appendix A A.7 ...
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This note was uploaded on 10/21/2008 for the course BCEE 343 taught by Professor Dr.ha during the Winter '08 term at Concordia Canada.
- Winter '08