Credit

945aebda-f8ed-4738-bf6e-113eea3772d7 18 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Credit

Credit for the core calulcation proceedure is given to Martin Kraska See here for original version: http://smath.info/file/NESDC

Templates for Beam Drawing

beam beam 01 - 11 - 110101 - 52 mat black 1 lightgray 14 mat 11001021 mat 14 mat :

These are the objects that can be placed in the modeller region to define the model.

s force force 0001 s * - 22 mat green 2 green 0.2 1 - 1 s * - 0011 s * - 1 - 1 s * - 42 mat (* green 2 green 24 mat 1104021 mat 14 mat :

support constraint w=w.0 1 - 01001 - 1 - 042 mat forestgreen 1 #5500ff00 14 mat 1101021 mat 14 mat :

sym constraint φ=0 000122 mat red 2 white 1 - 01022 mat #00000000 00000000024 mat 1103021 mat 14 mat :

I J dist distributed load 000 I - 1 J - 1042 mat blue 0 #550000ff 14 mat 1502021 mat 14 mat :

φ.1 φ.2 arc a 02 matrix : φ φ.1 φ.2 φ.1 30 ° * + range a a φ cos φ sin 12 mat stack : for a 31 line :

circle hinge 0 ° * 360 ° * arc eval black 0 white 14 mat 1101021 mat 14 mat :

s moment moment s - 10101 - s 1 - 42 mat red 2 #00000000 s - 1 0.8 s * - 1.2 0.8 s * - 0.8 s - 142 mat red 2 red 1 - (s - 1 0.8 s * - 1.2 0.8 s * - 0.8 1 s * - 142 mat * red 2 red 34 mat 1303021 mat 14 mat :

Vorlage beam support sym circle 11 dist 10 dist 01 dist 1 force 1 - force 1 - moment 1 moment 111 sys :

t.beam 1 :

t.fpos 8 :

Set "Vorlage" as template in the context menu of the modeler region.

t.cw 2 :

t.fneg 9 :

t.cφ 3 :

t.mpos 10 :

t.hinge 4 :

t.mneg 11 :

The items in the model are identified by template number.

t.qq 5 :

t.q0 6 :

t.0q 7 :

All of the t.__ variables are global. This is dangerous due to "t" beinging used for thickness. If these are to be Global they should be modified with #G so it is understood that they are global. Or they need to be incorporated into a function.

Create Modeller Input

Note: Modeller# is output

supports# MoE# I# w# w.p# Pt# Modeller# fModeller ***This creates our Modeller Input*** t 1 time : Initilize height counter h.prev# 0 ft * 1 l.0 / * : Create Supports length# supports# 1 supports# cols el supports# 11 el - 2 / 1 l.0 / * : Support# 05 matrix : n 1 supports# cols range type# supports# 2 n el : pos# supports# 1 n el 1 l.0 / * : t# t.cw type# 1 ≡ t.hinge type# 0 ≡ unknown cases : t# unknown ≡ unknown support type type# num2str at column n num2str concyat trace continue 21 line 0 if Support# Support# t# pos# 0 ft l.0 / * 0.2 length# * 0.2 length# * 15 mat stack eval : 51 line for h.prev# Support# 15 el : 51 line Create beam Beam# 05 matrix : t# t.beam : posx# supports# 1 supports# cols el supports# 11 el - 2 / 1 l.0 / * : length# supports# 1 supports# cols el supports# 11 el - (1 l.0 / * : height# MoE# I# * 1 F.0 l.0 2^* / (* length# 4^/ : posy# height# 2 / h.prev# + : length# supports# 1 supports# cols el supports# 11 el - (1 l.0 / * : Beam# Beam# t# posx# posy# length# height# 15 mat stack eval : h.prev# h.prev# height# + : 101 line Create Distributed Loads modeller input UDistModeller# 05 matrix : n 1 w# rows range t# t.qq : height# w# n el q.0 / : posx# supports# 1 supports# cols el supports# 11 el - 2 / 1 l.0 / * : posy# height# 2 / h.prev# + : length# supports# 1 supports# cols el supports# 11 el - (1 l.0 / * : UDistModeller# UDistModeller# t# posx# posy# length# height# 15 mat stack eval : h.prev# h.prev# height# + : 71 line for 31 line Create Partial / Varying Loads Create new matrix which splits up the trapazoidal loads into new columns in a new w.p matrix w.p## 40 matrix : n 1 w.p# cols range q.1# w.p# 1 n el q.0 / : x1# w.p# 2 n el l.0 / : q.2# w.p# 3 n el q.0 / : x2# w.p# 4 n el l.0 / : Create a uniform load q.unp# q.1# q.2# Min : Create triangular (varying) load q.vp1# q.1# q.unp# - : q.vp2# q.2# q.unp# - : Create conditional cases matrices for uniform and varying loads. Return empy matrix if not in use w.pi## q.unp# x1# q.unp# x2# 41 mat q.1# q.2# ≡ q.1# x1# q.2# x2# 41 mat q.1# 0 ≡ (q.2# 0 ≡ (| q.unp# q.vp1# x1# x1# q.unp# q.vp2# x2# x2# 42 mat cases eval : w.p## w.p## w.pi## augment eval : 121 line for Now use w.p## as the partial load matrix Create varying loads modeller input VDistModeller# 05 matrix : n 1 w.p## cols range t# t.qq w.p## 1 n el w.p## 3 n el ≡ t.q0 w.p## 1 n el w.p## 3 n el > t.0q w.p## 1 n el w.p## 3 n el < Unknown cases eval : height# w.p## 1 n el w.p## 3 n el Max : posx# w.p## 2 n el w.p## 4 n el + 2 / : posy# height# 2 / h.prev# + : length# w.p## 4 n el w.p## 2 n el - (: VDistModeller# VDistModeller# t# posx# posy# length# height# 15 mat stack eval : h.prev# h.prev# height# + : t# unknown ≡ unknown partial load w.p## num2str at column n num2str concyat trace continue 21 line 0 if 81 line for 81 line Point Loads Ptmodeller# 05 matrix : n 1 Pt# cols range F.p# Pt# 1 n el F.0 / : X.Fp# Pt# 2 n el l.0 / : F.p# 0 ≥ t# t.fpos : 11 line t# t.fneg : 11 line if height# F.p# : posx# X.Fp# : posy# height# 2 / h.prev# + : length# 0.1 height# * : Ptmodeller# Ptmodeller# t# posx# posy# length# height# 15 mat stack eval : 81 line for 31 line AssembleMatrix Modeller# Support# Beam# UDistModeller# VDistModeller# Ptmodeller# stack : 21 line Modeller# 1 time t - 121 line :

Process Info for Input into Solver

Note that N# and E# are outputs, out has been replaced with model# which is used in the function. Modeller is the input

model matrix: template type, x pos to center of width, y pos to center of height, width, height

Element matrix: [start node, end node, stiffness, dist load val start, dist. load value end]

Node matrix, N#: [x-position, Point Load value, Point Moment Value, support flag, support force, hinge flag

model# I# MoE# tol# E# N# fBeamPre *** This is the preprocessor - create nodes, elements, and loads **** t 1 time : Initialize the variable for the element matrix E# 0 : Initalize the variable for the nodes matrix N# 0 : build EI(x) and create nodes at beam ends beams# model# t.beam 1 findrows : Initilize the 'preliminary stiffness of beam segments matrix EI is given an initial value so that it can be used in a 'counter loop' for beams EI# 0 : A nodes matrix, containing nothing is created. We use '0' for the row becase we do not want anthing in the first element other wise the stack function will put a '0' as the first element, which is not correct Nodes will also be used in a 'counter' and therefore we are initilizing it the same as we do for the other variables nodes# 01 matrix : j 1 beams# rows range x.1# beams# j 2 el beams# j 4 el 2 / - : x.2# beams# j 2 el beams# j 4 el 2 / + : Below EI is in the equation so that it can be added for each iteration For example if 2 beams are stacked on top of eachother in the modeller add EI or we could use the height of the beam here to modify the E and I here in future. It works by adding to the EI# equation i.e. E*I*(x range) + E*I*(x range_2) if the input 'x' is within the x-range then the equations will add EI# EI# MoE# I# * 1 F.0 l.0 2^* / (* (x.1# x# ≤ (x# x.2# ≤ (& (* + : nodes# nodes# x.1# x.2# 21 mat stack eval : 91 line for x# EI# EI# : build q(x) and create nodes at distributed load ends initialize q# as 0 so that it can be use in a 'counter' for loads Stacked on top of each other q# 0 : items# t.qq 11 t.q0 10 t.0q 0133 mat : k 1 items# rows range dist# model# items# k 1 el 1 findrows : dist# 0 ≠ j 1 dist# rows range x.1# dist# j 2 el dist# j 4 el 2 / - : x.2# dist# j 2 el dist# j 4 el 2 / + : q# is created very similiar to how EI# is created, see notes above q# q# dist# j 5 el q.0 l.0 * F.0 / * items# k 3 el x# x.1# - x.2# x.1# - / (* items# k 2 el x.2# x# - x.2# x.1# - / * + (* x.1# x# ≤ (x# x.2# ≤ (& (* + : Nodes again are inculded in the equation as a 'counter' to add previous nodes and the new nodes for the distributed loads nodes# nodes# x.1# x.2# 21 mat stack eval : 71 line for 0 if 21 line for x# q# q# : create nodes at hinges, constraints and point loads k t.cw t.cφ t.hinge t.fpos t.fneg t.mpos t.mneg 17 mat items# model# k 1 findrows : items# 0 ≠ j 1 items# rows range nodes# nodes# items# j 2 el 11 mat stack eval : 11 line for 0 if 21 line for merge identical nodes tol## tol# l.0 / : nsort# nodes# sort : Initialize k:1 k 1 : Create and initilize the nodal matrix N# 11 el nsort# 1 el eval : N# 17 el 0 : j 2 nsort# rows range We don't use for statement with 'k' becuase we don't know how many values need to be adjusted to meet the tolerance criteria. So we initilized k above N# k 1 el nsort# j el - abs tol## > if the nodes are greater than tolerance then assign them to the N# (nodal matrix) k k 1 + : N# k 1 el nsort# j el eval : 31 line If they are not, then do nothing. Note that the N# matrix will not be assigned zero Rather nothing happens. i.e. there is no node added to N# becasue we are saying that the values are so close that this is really the same node, so don't add another node 041 line if 31 line for Create a function which determines if the input x-value is at a node (wihin tolerance) then return that node number x# n.N# node number for a given x value initilize a variable for a counter (use nn) nn# 0 : j 1 N# rows range Check if the input x is close enough (within tolerance) to node j x# N# j 1 el - abs tol## < if x is within tolerance then set it equal to that node number nn# j : 21 line 0 if 21 line for nn# 51 line : create elements. Mitigate zero stiffness to a low value Initilize an E# matrix E# 05 matrix : j 1 N# rows 1 - range EI of the jth element Send the midpoint of the element to the EI# function. Note that we choose the max of EI or a very low value for stiffness (to avoid crashing) EI.e# N# j 1 el N# j 1 + 1 el + 2 / EI# 0.0000001 MoE# * I# * 1 F.0 l.0 2^* / * 12 mat max eval : Send element points to the q function to evaluate loads at each end of the element (noting the tolerance) q.I# N# j 1 el tol## + q# : q.J# N# j 1 + 1 el tol## - q# : Create the element with its start number, end number, Stiffness (EI) and its distributed load value at each end E# E# j j 1 + EI.e# q.I# q.J# 15 mat stack eval : 111 line for Add nodal items: template number, N column (position in N matirx), value Note that t.cw is on twice to account for a displaced (vertically) support Fill in item (values) by defining below items# t.cw 41 w constraint flag t.cw 5 item# 3 el w.0 l.0 / * - w constraint value t.cφ 61 φ constraint flag t.fpos 2 item# 5 el F value t.fneg 2 item# 5 el - F value t.mpos 3 item# 4 el item# 5 el (* M value t.mneg 3 item# 4 el item# 5 el - (* M value 74 mat : k 1 items# rows range Build a matrix called 'tmp' which contains nodal items defined above tmp# model# items# k 1 el 1 findrows : Check if the nodal item exists, if it does not exist use 'continue' to end the current iteration of the loop tmp# 0 ≠ 1 continue if j 1 tmp# rows range Set item equal to the 'j' row of the tmp matrix item# tmp# j row : Send the 'X' position of the item to the n.N# function, which determines which node (i.e. which row) of the nodal matrix that point load belongs to n# item# 2 el n.N# : The 2nd column of the items matrix defines which column the 'value' (meaning the nodal force (i.e. point load) should be placed in the Nodal matrix N# pos# items# k 2 el : Set value of nodal force which will be placed in the nodal matrix value# items# k 3 el : Fill in the nodal matrix with location in row 1, and value of nodal forces in other rows N# n# pos# el value# eval : 131 line for 61 line for add hinges hinges# model# t.hinge 1 findrows : hinges# 0 ≠ j 1 hinges# rows range Send the x value for the hinge to the n.N# equation to find which node number the hinge is at. n# hinges# j 2 el n.N# : Create a tmp matrix which the 1st column is the row number of the element and the following columns contain the element information. Using 'range(1..rows(E#)) creates a column matrix starting with 1 to number of rows in E# This means that the number of rows will match E# and also number the rows. tmp_2# 1 E# rows range E# augment : define 'er' -> search for the node number on (i.e. the start node of the element) then return the element number. Note that we first return an entire row using findrows then we return the first colum in that row with the 'sub-1' notation er# tmp_2# n# 2 findrows 1 el eval : Add new node at the same location. Then create a 0 length element between them Note -> stack this node at the bottom, must fill in with zeros to match vector size N# N# hinges# j 2 el 00000017 mat stack : Assign the node number of this new node to n.h# Note that this will always be at the bottom of the N# matrix so use rows(N) for the node number n.h# N# rows : Add hinge to the element matrix (type is recognized by zero lenght in FEA) Note that n# and n.h# will have the same x-value and thus a 0 length E# E# n# n.h# MoE# I# * 1 F.0 l.0 2^* / * 0015 mat stack eval : Modify the element to the right of the 0 length 'hinge' element so that the start node of the element to the right is now n.h# which is the right side of the 0 length hinge element This way the element doesn't span over the 0 length hing element E# er# 1 el n.h# : 251 line for 0 if 1 time t - 531 line :

Beam Solver

Inputs: N# (nodal matrix) and E# (element matrix) Outputs: Nres# and Eres#

BeamSol(N,E,Nres,Eres) Beam FEA solver. N,E node and element matrices. Each line in N has the entries
(x, F, M, w-flag, w-value, φ-flag, φ-value). Flags=1 means constraint to given value. 
Each line in E has the entries (I, J, EI, qI, qJ). Zero length elements are hinges with w-stiffnes EI.
Nres are nodal results (x, w, φ, F, M, RF, RM), Eres are element results for plotting with the columns 
(x, q, Q, M, φ, w) N# E# Nres# Eres# fBeamSol t 1 time : n.e E# rows : n.n N# rows : K 2 n.n * 2 n.n * matrix : F 2 n.n * 1 matrix : u 2 n.n * 1 matrix : provide functions for result computation x w 120 w.I * l 3^* EI * x x x 340 EI * 2 w.J - w.I + (* - l φ.J φ.I + (* + (* l 4^q.J * + (* l 2^7 l 2^* q.I * x x q.J * x - 5 l * + (q.I * + (* - (* + (* - 260 EI * 3 w.J - w.I + (* - l φ.J 2 φ.I * + (* + (* l 4^q.J * + (* 3 l 4^* q.I * + (l * + (* 120 φ.I * l 3^* EI * - (* + 120 l 3^* EI * / : x φ 120 φ.I * EI * l 3^* x x 5 x * x q.J * x - 4 l * + (q.I * + (* l 2^* 3340 EI * 2 w.J - w.I + (* - l φ.J φ.I + (* + (* l 4^q.J * + (* 7 l 4^* q.I * + (* - (* 2260 EI * 3 w.J - w.I + (* - l φ.J 2 φ.I * + (* + (* l 4^q.J * + (* 3 l 4^* q.I * + (* l * + (* - 120 EI * l 3^* / : x M 260 EI * 3 w.J - w.I + (* - l φ.J 2 φ.I * + (* + (* l 4^q.J * + (* 3 l 4^* q.I * + (l * x 10 x * x q.J * x - 3 l * + (q.I * + (* l 2^* 3340 EI * 2 w.J - w.I + (* - l φ.J φ.I + (* + (* l 4^q.J * + (* 7 l 4^* q.I * + (* - (* + 60 l 3^* / - : x Q 340 EI * 2 w.J - w.I + (* - l φ.J φ.I + (* + (* l 4^q.J * + (* 7 l 4^* q.I * + 10 x * x q.J * x - 2 l * + (q.I * + (* l 2^* - 20 l 3^* / : Element stiffness (beam or hinge) and element load vector EI l K.e l 0 > 12 EI * l 3^/ 6 EI * l 2^/ - 12 EI * l 3^/ - 6 EI * l 2^/ - 6 EI * l 2^/ - 4 EI * l / 6 EI * l 2^/ 2 EI * l / 12 EI * l 3^/ - 6 EI * l 2^/ 12 EI * l 3^/ 6 EI * l 2^/ 6 EI * l 2^/ - 2 EI * l / 6 EI * l 2^/ 4 EI * l / 44 mat EI 0 EI - 00000 EI - 0 EI 0000044 mat if : q.I q.J l f.e l 3 q.J * 7 q.I * + (* 20 / l 2^2 q.J * 3 q.I * + (* 60 / - l 7 q.J * 3 q.I * + (* 20 / l 2^3 q.J * 2 q.I * + (* 60 / 41 mat : Assemble global stiffness and element loads i.e 1 E# rows range I E# i.e 1 el : J E# i.e 2 el : EI E# i.e 3 el : q.I E# i.e 4 el : q.J E# i.e 5 el : l N# J 1 el N# I 1 el - : j i.g j 2 ≤ (0 ≠ (j 21 - I + (* + (* j 2 ≤ (0 ≡ (j 22 - J + (* + (* + (: i 14 range j 14 range K i i.g j i.g el K i i.g j i.g el EI l K.e i j el + eval : for F i i.g el F i i.g el q.I q.J l f.e i el + eval : 21 line for 81 line for add concentrated loads and constraints i.n 1 N# rows range F 2 i.n * 1 - el F 2 i.n * 1 - el N# i.n 2 el + : F 2 i.n * el F 2 i.n * el N# i.n 3 el + : u 2 i.n * 1 - el N# i.n 4 el N# i.n 5 el * : u 2 i.n * el N# i.n 6 el N# i.n 7 el * : c 2 i.n * 1 - el N# i.n 4 el : c 2 i.n * el N# i.n 6 el : 61 line for F.e F eval : reduce the system using constraints cc 12 n.n * range c augment : constr cc 12 findrows 1 col eval : free cc 02 findrows 1 col eval : F F K u * - eval : i 1 free rows range F.R i el F free i el el : j 1 free rows range K.R i j el K free i el free j el el : 11 line for 21 line for solve the system u.R K.R 1 -^F.R * eval : free rows 1 ≡ u.R u.R 11 mat : 0 if expand solution to full system i 1 free rows range u free i el el u.R i el : for Nodal (DOF) results: x, w, φ, F, M, FR, MR Nres# 07 matrix : R K u * F.e - eval : j 1 n.n range Nres# Nres# N# j 1 el u 2 j * 1 - el u 2 j * el ° / F.e 2 j * 1 - el F.e 2 j * el R 2 j * 1 - el R 2 j * el 17 mat stack eval : for Element results: x, q, Q, M, φ, w Eres# 06 matrix : n 8 : i.e 1 n.e range I E# i.e 1 el : J E# i.e 2 el : 12 mat x.I N# I 1 el : x.J N# J 1 el : q.I E# i.e 4 el : q.J E# i.e 5 el : w.I u 2 I * 1 - el : w.J u 2 J * 1 - el : φ.I u 2 I * el : φ.J u 2 J * el : 42 mat l x.J x.I - : EI E# i.e 3 el eval : l 0 > j 0 n range x l j n / * : q q.J x l / * q.I l x - l / * + : Eres# Eres# x x.I + q x Q x M x φ ° / x w 16 mat stack eval : 31 line for 0 if 51 line for 1 time t - 391 line :

Beam Post Processor

fBeamPost[Res,T,P) Beam FEA postprocessing. Res: element results from BeamSol(), 
T: Modeller template, P: Modeller predefined layoutE Res# T# P# fBeamPost t 1 time : M Res# 4 col - : Q Res# 3 col - : w Res# 6 col (: x Res# 1 col (: q Res# 2 col - : M.max M max M min abs 0.001 13 mat max : Q.max Q max Q min abs 0.001 13 mat max : w.max w max w min abs 0.001 13 mat max : q.max q max q min abs 0.001 13 mat max : P# 101405005020555001003055 - 50010040140 - 5005045 mat : Axes x 1 el 0 x x rows el 022 mat black 1 black x 1 el 1 - x 1 el 122 mat black 1 black 24 mat : T# q Axes x q q.max / augment x x rows el 0 x 1 el 022 mat stack blue 1 #550000ff 14 mat stack eval 15005021 mat 14 mat Q Axes x Q Q.max / augment x x rows el 0 x 1 el 022 mat stack forestgreen 1 #5500ff00 14 mat stack eval 150010021 mat 14 mat Q Axes x M M.max / augment x x rows el 0 x 1 el 022 mat stack red 1 #55ff0000 14 mat stack eval 150010021 mat 14 mat w Axes x w w.max / augment black 2 #00000000 14 mat stack eval 15005021 mat 14 mat 41 sys : 1 time t - 141 line :

M# c# Absmax D M# c# col : D min abs D max 12 mat max 21 line :

Nhead x w φ F M S:F.R S:M.R S:'l.0 S:'w.0 S:'° S:'F.0 S:'F.0*'l.0 S:'F.0 S:'F.0*'l.0 27 mat :

Input

Input

plf lbf ft / :

Set length unit

l.0 1 ft * :

Set force unit

F.0 1 kip * :

Set displacement unit

w.0 1 in * :

Eventually change sysmbols for deflection and length (update all symbols in calc)

q.0 1 F.0 l.0 / * :

Set distributed load unit

Set beam number to keep track of reactions increase for each beam case

bm 1 :

supports 0 ft * 10 ft * 1122 mat :

0=hinge, 1=pin support, 2= fixed (built in) support. Use hinge for cantilever Enter from 0' to end of beam -> left to right

Support / Hinge

MoE

MoE 29000 ksi * :

MoI

I 100 in 4^* :

Uniform Load

w 1 kip ft / * 11 mat :

On all spans (use multiple rows for multiple input)

Partial Loads

w.p 0 kip ft / * 0 ft * 0 kip ft / * 0 ft * 41 mat :

Enter wb in top row

Enter b in second row

Enter we in third row

Enter e in bottom row

Point Loads

Pt 0 kip * 0 ft * 21 mat :

Node Tolerance

tol 1 in * :

Function Calls

supports MoE I w w.p Pt Modeller fModeller 0.004 sec *

Modeller I MoE tol E N fBeamPre 0.01 sec *

N E Res.N Res.E fBeamSol 0.027 sec *

Res.E T P fBeamPost 0.009 sec *

M.max Res.E 4 Absmax F.0 * l.0 * :

V.max Res.E 3 Absmax F.0 * :

y.max Res.E 6 Absmax l.0 * :

w.max Res.E 2 Absmax F.0 l.0 / * :

Verify constants are unitless:

q.0 l.0 * F.0 / 1

w.0 l.0 / 0.0833

MoE I * F.0 l.0 2^* / 20138.8889

Results

w.max kip ft / 1

V.max kip 5

NO GRAPHS

M.max kip ft * 12

y.max in 0.078

w.max y.max V.max M.max Res.N N E tol Pt w I MoE supports bm 'q.0 'w.0 'F.0 'l.0 'plf Nhead Absmax fBeamPost fBeamSol fBeamPre fModeller t.0q t.q0 t.qq t.mneg t.hinge t.mpos t.cφ t.fneg t.cw t.fpos t.beam moment circle arc dist sym support force beam lastError w.max y.max V.max M.max T Res.N N tol Pt w.p w I MoE bm 'q.0 'w.0 'F.0 'l.0 'plf Nhead Absmax fBeamPost fBeamSol fBeamPre fModeller t.0q t.q0 t.qq t.mneg t.hinge t.mpos t.cφ t.fneg t.cw t.fpos t.beam Vorlage arc lastError w.max y.max V.max M.max tol Pt I MoE bm 'q.0 'w.0 'F.0 'l.0 'plf t.0q t.q0 t.qq t.mneg t.hinge t.mpos t.cφ t.fneg t.cw t.fpos t.beam

Res.N 1 csort eval
0.000	0.000	-0.119	5.000	-8.333	-5.000	0.000
10.000	0.000	0.119	5.000	8.333	-5.000	0.000
#
x	w	φ	F	M	S:F.R	S:M.R
S:'l.0	S:'w.0	S:'°	S:'F.0	S:'F.0*'l.0	S:'F.0	S:'F.0*'l.0
#
#
#

position

w

displacement

φ

slope in °

F, M

external loads, including contri- butions of distri- buted loads

F.R

Support reactions

M.R

Keep Track of Beam Reactions F.R Res.N 1 csort eval 6 col : n 1 F.R rows range R.bm bm n el F.R n el : 11 line for 31 line