/*
* ==================================================================
* Test input file for bridge design rule checking wsing 2D-beam
* element and static analysis
*
* Written by: Wane-Jang Lin June 1995
* ==================================================================
*/
print "*** DEFINE PROBLEM SPECIFIC PARAMETERS \n\n";
NDimension = 2;
NDofPerNode = 3;
MaxNodesPerElement = 2;
StartMesh();
div_no = 10;
print "*** GENERATE GRID OF NODES FOR FE MODEL \n\n";
length = 56.70 ft;
cov_dis = 10.35 ft;
dL = length/div_no;
x = 0 ft; y = 0 ft;
for( i=1; x<=length ; i=i+1 ) {
AddNode(i, [x, y]);
x = x+dL;
}
print "*** ATTACH ELEMENTS TO GRID OF NODES \n\n";
elmt = 1;
x = 0 ft;
for( i=1; i<=div_no ; i=i+1 ) then {
if( x(length-cov_dis) ) {
AddElmt( elmt, [i, i+1], "girder1");
} else {
AddElmt( elmt, [i, i+1], "girder2");
}
elmt = elmt+1;
x = x+dL;
}
print "*** DEFINE ELEMENT, SECTION AND MATERIAL PROPERTIES \n\n";
I1 = 17268.4 in^4; y1 = 29.40 in; area1 = 38.3 in^2;
I2 = 25700.1 in^4; y2 = 27.31 in; area1 = 48.8 in^2;
ElementAttr("girder1") { type = "FRAME_2D";
section = "no_cover";
material = "STEEL3";
}
ElementAttr("girder2") { type = "FRAME_2D";
section = "cover";
material = "STEEL3";
}
SectionAttr("no_cover") { Izz = I1;
area = area1;
depth = 33.09 in;
width = 11.51 in;
}
SectionAttr("cover") { Izz = I2;
area = area2;
depth = 33.09 in;
width = 11.51 in;
}
/*
* ======================================
* Setup Boundary Conditions [dx, dy, rz]
* ======================================
*/
FixNode(1, [1, 1, 0]);
FixNode(div_no+1, [0, 1, 0]);
/*
* =====================================
* Compile and Print Finite Element Mesh
* =====================================
*/
EndMesh();
PrintMesh();
SetUnitsType("US");
stiff = Stiff();
lu = Decompose(stiff);
/*
* =====================================
* Add Dead Nodal Loads [Fx, Fy, Mz]
* =====================================
*/
weight = 0.199 kips/ft + 0.868 kips/ft;
load = weight*dL;
for( i=2; i<=div_no; i=i+1 ) {
NodeLoad( i, [0 kips, -load, 0 kips*ft]);
}
NodeLoad( 1, [0 kips, -load/2, 0 kips*ft]);
NodeLoad( div_no+1, [0 kips, -load/2, 0 kips*ft]);
eload = ExternalLoad();
displ = Substitution(lu, eload);
max_displ_dead = GetDispl([div_no/2+1],displ);
max_mom_dead = GetStress([div_no/2],displ);
max_sh_dead = GetStress([1],displ);
cover_mom_dead = GetStress([2],displ);
PrintMatrix(max_displ_dead,max_mom_dead,max_sh_dead,cover_mom_dead);
/* Get Moment Diagram */
moment_dead = Zero([ div_no+1 , 1 ]);
for( i=1 ; i<=div_no ; i=i+1 ) {
temp = GetStress([i],displ);
if( i == 1 ) { moment_dead[1][1] = temp[1][3]; }
moment_dead[i+1][1] = temp[2][3];
}
PrintMatrix(moment_dead);
/* Zero-out dead loadings */
for( i=2; i<=div_no; i=i+1 ) {
NodeLoad( i, [0 kips, load, 0 kips*ft]);
}
NodeLoad( 1, [0 kips, load/2, 0 kips*ft]);
NodeLoad( div_no+1, [0 kips, load/2, 0 kips*ft]);
/*
* =====================================
* Add Live Truck Load [Fx, Fy, Mz]
* =====================================
*/
step = div_no+1;
influ_mid_mom = Zero([ step , 1 ]);
influ_end_sh = Zero([ step , 1 ]);
envelop_mom_live = Zero([ step , 1 ]);
HS20 = 72 kips;
mom_elmt = div_no/2;
sh_elmt = 1;
for( i=1 ; i<=step ; i=i+1 ) {
NodeLoad( i, [0 kips, -HS20, 0 kips*ft] );
eload = ExternalLoad();
displ = Substitution( lu, eload );
mid_mom = GetStress( [mom_elmt], displ );
end_sh = GetStress( [sh_elmt], displ );
if( i == 1 ) then {
mom_rang = GetStress( [i], displ );
} else {
mom_rang = GetStress( [i-1], displ );
}
/* Get moment influence line at the middle of span */
influ_mid_mom[i][1] = mid_mom[2][3];
/* Get Shear Influence line at the end support */
influ_end_sh[i][1] = end_sh[1][2];
/* Create envelope of moment influence line at the middle of span */
if( i == 1 ) then {
envelop_mom_live[1][1] = mom_rang[1][3];
} else {
envelop_mom_live[i][1] = mom_rang[2][3];
}
if( i == mom_elmt+1 ) {
max_displ_live = GetDispl([mom_elmt+1],displ);
max_mom_live = GetStress([mom_elmt],displ);
}
if( i == sh_elmt ) {
max_sh_live = GetStress([sh_elmt],displ);
max_sh_live[1][2] = max_sh_live[1][2] + HS20;
influ_end_sh[1][1] = HS20;
}
if( i == 3 ) {
cover_mom_live = GetStress([2],displ);
}
NodeLoad( i, [0 kips, HS20, 0 kips*ft] );
}
PrintMatrix(max_displ_live,max_mom_live,max_sh_live,cover_mom_live);
PrintMatrix(influ_mid_mom, influ_end_sh, envelop_mom_live);
/*
* ============================
* Results for DL + (LL+Impact)
* ============================
*/
impact = 1 + 50/(56.7+125);
print "\nimpact factor = ",impact,"\n";
max_displ = max_displ_dead + impact*max_displ_live;
max_mom = max_mom_dead + impact*max_mom_live;
max_sh = max_sh_dead + impact*max_sh_live;
cover_mom = cover_mom_dead + impact*cover_mom_live;
PrintMatrix(max_displ,max_mom,max_sh,cover_mom);
/*
* =========================================================
* WSD Code Checking for Deflections and Stress Requirements
* =========================================================
*/
print "\n\nSTART ASD CODE CHECKING::\n";
/* Deflection Checking */
if( -impact*max_displ_live[1][2] > (1/800)*length ) then {
print "\n\tWarning: (LL+I) deflection exceeds 1/800 span\n";
} else {
print "\n\tOK : (LL+I) deflection less than 1/800 span\n";
}
/* Moment Stress Checking */
my_material = GetMaterial([1]);
my_section = GetSection([1]);
/* max stress without cover plate */
stress1 = cover_mom[2][3]*y1/I1;
/* max stress with cover plate (in the middle of span) */
stress2 = max_mom[2][3]*y2/I2;
if( stress1 > 0.55*my_material[3][1] ) then{
print "\n\tWarning : moment stress without cover plate larger than 0.55*Fy\n";
} else {
if( stress2 > 0.55*my_material[3][1] ) then{
print "\n\tWarning : moment stress with cover plate larger than 0.55*Fy\n";
} else {
print "\n\tOK : moment stress less than 0.55*Fy\n";
}
}
/* Shear Stress Checking */
shear = max_sh[1][2]/my_section[11][1];
if( shear > 0.33*my_material[3][1] ) then{
print "\n\tWarning : shear stress larger than 0.33*Fy\n";
} else {
print "\n\tOK : shear stress less than 0.33*Fy\n";
}
quit;
In this example, we check the analysis result with AASHTO WSD specification.
item [1] : The impact factor for live load is based on the formula AASHTO Eq. (3-1) I = 50/L+125 in which I = impact fraction (maximum 30 percent) and L = length in feet of the portion of the span.
item [2] : The deflection checking is based on AASHTO Art.10.6.2, the deflection due to service live load plus impact shall not exceed 1/800 of the span.
item [3] : The allowable stress is 0.55 X Fy for tension and compression member, 0.33 X Fy for shear in web.