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FINITE ELEMENT SPREADSHEET

Program Description:

This is an MS-Excel spreadsheet to analyze 2-Dimensional frame and truss problems.

The frame resides in the x-y plane and consists of a number of members. Each member is straight, defined

by the nodes at each end. The number of nodes and members is fixed for a gien spreadsheet.

Each node must be connected to the structure.

Each member must hae a node at each end !cannot hae the same node at each end of a member"

#$ight-hand rule# defines x,y % z axes and shear % moment sign conention.

&nputs are'

(ode coordinates, in x-y plane

Member connectiity !)hich t)o nodes define member end points"

Member properties, *xx, &zz, E+mod !cross-section area, moment-of-inertia, and modulus of elasticity

Support springs, at node locations only. Springs may be x, y !deflection in x%y" or z !rotation in z"

(ode loads, x, y, Mz !forces in x%y, moment about z"

Member uniform load !a distributed load of constant alue along the length of and perpendicular to a

(ote that the calculated alues at a member end may not be maximum alues for that member.

alculated $esults'

Support $eactions !x%y forces, z-moments"

(ode displacements !x%y displacements, z-rotation"

Member end forces !*xial force, shear force, moment" - (ote that the calculated alues at a member

*ll intermediate calculations steps and alues are aailable.

This program is a )orboo consisting of three !/" )orsheets, described as follo)s'

Worksheet Tab ontents

Description This documentation sheet

EM inite Element *nalysis

0lot Member geometry plot

Program Ass!mptions an" Limitations:

1. This program uses the #stiffness matrix# method of analysis and the follo)ing basic analysis assumptions'

a. Members are isotropic and homogeneous !*xx, &zz, and E+mod are constant for entire length".

b. Small deflections !not significant enough to alter the geometry of the problem".

c. Stress is linearly proportional to strain, ie' elastic.

d. Shear deformations are not included.

2. * ertical load, horizontal load, and externally moment may be applied to any of the oints of the frame.

3oint loads are to be applied in #global# axes directions. (ote' 3oint loads applied directly at supports are mere

added directly to support reactions and are not reflected in member end force alues.

Proce"!re #se" b$ FEM Sprea"sheet:

1. 4ser inputs node geometry % loads, and member connectiity, properties % uniform loading

2. Spreadsheet calculates fixed-end moments !EM5s" and shears for each member due to applied me

/. Spreadsheet calculates local member stiffness matrix for each member. !See EM cells **6'*12 fo

Members that are not needed can be #inactiated# by setting properties *xx, &zz and8or E+mod to approachzero

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9. Spreadsheet calculates coordinate transformation matrix for each member !transforms loca

:. Transforms local member stiffness matrix into global stiffness componants for each member.

;.

6. &nerts the global stiffness matrix !using Excel5s #M&(

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ember"

nd may not be maximum alues for that member.

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l geometry to global"

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FI/#RE 0 12ST3R4 5#ILDIN/ E6AMPLE 1; (DE, /6 MEMFE$ S0$E*DSGEET

This spreadsheet is proided for illustratie teaching purpose only, and is not intended for use in any specific proect.# *nyone maing use

of the information contained in this spreadsheet does so at his8her o)n ris and assumes any and all resulting liability arising therefrom.

BradC

(DE D*T*' Support Springs &nput orces Support $eactions utput Deflect

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Disc%aimer:

This sprea"sheet is pro&i"e" 'or i%%!strati&e teaching p!rpose on%$( an" is not in

An$one making !se o' the in'ormation containe" in this sprea"sheet "oes so ata%% res!%ting %iabi%it$ arising there'rom*

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ten"e" 'or !se in an$ speci'ic pro)ect*+

his,her o-n risk an" ass!mes an$ an"