Beam Anal
Beam Anal
Beam Anal
Program Description:
"BEAMANAL" is a spreadsheet program written in MS-Excel for the purpose of analysis of either single-span or
continuous-span beams subjected to virtually any type of loading configuration. Four (4) types of single-span beams
and two (2) through (5) span, continuous-span beams, considered. Specifically, beam end reactions as well as the
maximum moments and deflections are calculated. Plots of both the shear and moment diagrams are produced,
as well as a tabulation of the shear, moment, slope, and deflection for the beam or each individual span. Also, for
steel single-span beams an AISC 9th Edition (ASD) Code check can be performed for X-axis bending and shear.
This program is a workbook consisting of four (4) worksheets, described as follows:
Worksheet Name
Description
Doc
Single-Span Beam
Single-Span Beam & Code Check
Continuous-Span Beam
Formulas Used to Determine Shear, Moment, Slope, and Deflection in Single-Span Beams
For Uniform or Distributed Loads:
Loading functions for each uniform or distributed load evaluated at distance x = L from left end of beam:
FvL = -wb*(L-b-(L-e)) + -1/2*(we-wb)/(e-b)*((L-b)^2-(L-e)^2)+(we-wb)*(L-e)
FmL = -wb/2*((L-b)^2-(L-e)^2) + -1/6*(we-wb)/(e-b)*((L-b)^3-(L-e)^3)+(we-wb)/2*(L-e)^2
FL = -wb/(6*E*I)*((L-b)^3-(L-e)^3) + -1/(24*E*I)*(we-wb)/(e-b)*((L-b)^4-(L-e)^4)+(we-wb)/(6*E*I)*(L-e)^3
FL = -wb/(24*E*I)*((L-b)^4-(L-e)^4) + -1/(120*E*I)*(we-wb)/(e-b)*((L-b)^5-(L-e)^5)+(we-wb)/(24*E*I)*(L-e)^4
Loading functions for each uniform or distributed load evaluated at distance = x from left end of beam:
If x >= e:
Fvx = -wb*(x-b-(x-e)) + -1/2*(we-wb)/(e-b)*((x-b)^2-(x-e)^2)+(we-wb)*(x-e)
Fmx = -wb/2*((x-b)^2-(x-e)^2) + -1/6*(we-wb)/(e-b)*((x-b)^3-(x-e)^3)+(we-wb)/2*(x-e)^2
Fx = -wb/(6*E*I)*((x-b)^3-(x-e)^3) + -1/(24*E*I)*(we-wb)/(e-b)*((x-b)^4-(x-e)^4)+(we-wb)/(6*E*I)*(x-e)^3
Fx = -wb/(24*E*I)*((x-b)^4-(x-e)^4) + -1/(120*E*I)*(we-wb)/(e-b)*((x-b)^5-(x-e)^5)+(we-wb)/(24*E*I)*(x-e)^4
else if x >= b:
Fvx = -wb*(x-b) + -1/2*(we-wb)/(e-b)*(x-b)^2
else:
Fvx = 0
Fmx = -wb/2*(x-b)^2 + -1/6*(we-wb)/(e-b)*(x-b)^3-(x-e)^3
else:
Fmx = 0
Fx = -wb/(6*E*I)*(x-b)^3 + -1/(24*E*I)*(we-wb)/(e-b)*(x-b)^4
Fx = 0
else:
Fx = -wb/(24*E*I)*(x-b)^4 + -1/(120*E*I)*(we-wb)/(e-b)*(x-b)^5
Fx = 0
else:
For Point Loads:
Loading functions for each point load evaluated at distance x = L from left end of beam:
FvL = -P
FmL = -P*(L-a)
FL = -P*(L-a)^2/(2*E*I)
FL = P*(L-a)^3/(6*E*I)
Loading functions for each point load evaluated at distance = x from left end of beam:
If x > a:
Fvx = -P
else:
Fmx = -P*(x-a)
else:
Fx = -P*(x-a)^2/(2*E*I)
else:
Fx = P*(x-a)^3/(6*E*I)
else:
Fvx =
Fmx =
Fx =
Fx =
0
0
0
0
Fvx =
Fmx =
Fx =
Fx =
0
0
0
0
(continued)
o =
-1/L*(FmL)
0
1/L*(FL)+L/(6*E*I)*(FmL)
0
Propped beam:
Vo = -3*E*I/L^3*(FL)-3*E*I/L^2*(FL)
Mo = 0
o = 3/(2*L)*(FL)+1/2*(FL)
0
Fixed beam:
Vo =
Mo =
o =
o =
Cantilever beam:
Vo =
Mo =
o =
o =
-12*E*I/L^3*(FL)-6*E*I/L^2*(FL)
6*E*I/L^2*(FL)+2*E*I/L*(FL)
0
0
0
0
-(FL)
-(FL)-L*(FL)
Summations of shear, moment, slope, and deflection at distance = x from left end of beam:
Shear:
Moment:
Slope:
Deflection:
Vx =
Mx =
x =
x =
Vo+(Fvx)
Mo+Vo*x+(Fmx)
o+Mo*x/(E*I)+Vo*x^2/(2*E*I)+(Fx)
-(o-o*x-Mo*x^2/(2*E*I)-Vo*x^3/(6*E*I)+(Fx)
Reference:
"Modern Formulas for Statics and Dynamics, A Stress-and-Strain Approach"
by Walter D. Pilkey and Pin Yu Chang, McGraw-Hill Book Company (1978)
Note:
"Dummy" spans are used to model the left end and right end support conditions for the beam. A pinned
end is modeled as a very flexible span (very long length and very small inertia). A fixed end is modeled
as a very stiff span (very short length and very large inertia). Thus, the theoretical number of spans used
is = N + 2.
By writing an equation for each pair of consecutive spans and introducing the known values (usually zero)
of end moments, a system of (N+1) x (N+1) simultaneous equations can be set up to solve for the
unknown support moments.
Reference:
AISC Manual of Steel Construction - Allowable Stress Design (ASD) - 9th Edition (1989), page 2-294
"BEAMANAL.xls" Program
Version 2.0
Subject:
Originator:
##
Input Data:
##
Beam Data:
Span Type? Simple
Span, L = 20.0000 ft.
Modulus, E = 29000 ksi
Inertia, I = 391.00 in.^4
##
a
+P
Propped Beam
##
+M
##
+wb
+w ##
L
#
#
kips/ft.
End
wb (kips/ft.)
e (ft.)
we (kips/ft.)
RL =
ML =
#2:
#3:
+M(max) =
-M(max) =
#4:
#5:
#6:
-(max) =
+(max) =
(ratio) =
#7:
#8:
a (ft.)
#1: 10.0000
RR
Nomenclature
#1:
Point Loads:
##
P (kips)
20.00
Results:
Reactions:
10.50 k
RR =
N.A.
MR =
Maximum Moments:
@x=
102.50 ft-k
0.00 ft-k
@x=
Maximum Deflections:
-0.524 in
@x=
0.000 in
@x=
L/458
10.50 k
N.A.
#
#
#
10.00 ft
0.00 ft
#
#
#
10.00 ft
0.00 ft
#
#
#
#
Shear Diagram
15.00
#2:
#3:
#
#
10.00
19.2000
18.4000
17.6000
16.8000
16.0000
15.2000
14.4000
13.6000
12.8000
12.0000
11.2000
9.6000
10.4000
8.8000
8.0000
7.2000
6.4000
5.6000
4.8000
-5.00
4.0000
#9:
0.00
3.2000
#8:
#
2.4000
#7:
5.00
1.6000
#6:
0.8000
She ar (k ips)
#5:
0.0000
#4:
#10:
#
#
100.00
80.00
60.00
20.0000
19.2000
18.4000
17.6000
16.8000
16.0000
15.2000
14.4000
13.6000
12.8000
12.0000
x (ft.)
11.2000
10.4000
8.8000
8.0000
7.2000
6.4000
5.6000
4.8000
#
4.0000
0.00
3.2000
20.00
2.4000
1.6000
40.00
0.8000
#4:
M (ft-kips)
Moment Diagram
120.00
0.0000
#3:
c (ft.)
#14:
#15:
x (ft.)
-15.00
#13:
#2:
#
#
9.6000
#12:
#1:
#
#
-10.00
#11:
Moments:
20.0000
b (ft.)
RL
Cantilever Beam
Start
Distributed:
+we ##
Fixed Beam
E,I
Beam Loadings:
Full Uniform:
w = 0.0500
##
Simple Beam
#
#
#
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"BEAMANAL.xls" Program
Version 2.0
Input Data:
##
##
Beam Data:
Span Type? Simple
Span, L = 20.0000
Modulus, E = 29000
Inertia, Ix = 391.00
Beam Size = W12x50
Yield, Fy =
36
Length, Lb = 20.0000
Coef., Cb =
1.00
##
e
ft.
##
a
+P
ksi
in.^4
##
Simple Beam
Propped Beam
##
+M
+we
##
+wb
ksi
Fixed Beam
+w
ft.
E,I
RL
Cantilever Beam
RR
Nomenclature
Beam Loadings:
Full Uniform:
w = 0.0500
b (ft.)
#
#
#
#
kips/ft.
Start
Distributed:
##
wb (kips/ft.)
End
e (ft.)
we (kips/ft.)
Point Loads:
a (ft.)
10.0000
P (kips)
20.00
#1:
#1:
#2:
#2:
#3:
#3:
#4:
#4:
#5:
#5:
#6:
#6:
#7:
#7:
#8:
#8:
#9:
#10:
#1:
#11:
#2:
#12:
#3:
#13:
#4:
#14:
#15:
Moments:
c (ft.)
M (ft-kips)
Results:
End Reactions:
RL = 10.50
MxL =
N.A.
Maximum Moments:
+Mx(max) = 102.50
-Mx(max) =
0.00
kips
ft-kips
ft-kips
ft-kips
RR =
MxR =
x=
@x=
@
10.50
N.A.
10.00
0.00
kips
ft-kips
ft.
ft.
#
#
#
#
#
#
#
#
#
Maximum Deflections:
-(max) = -0.524
+(max) = 0.000
(ratio) = L/458
in.
in.
x=
@x=
@
10.00
0.00
ft.
ft.
#
#
#
#
#
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"BEAMANAL.xls" Program
Version 2.0
Job Name:
Job Number:
Checker:
c
Input Data:
e
b
Beam Data:
No. Spans, N =
Left End =
Right End =
Modulus, E =
a
+P
2
Pinned
Pinned
29000
Support #1
Span #1
Span #2
Span #3
Span #4
Span #5
+M
+we
+wb
Support #3
+w
ksi
2
2
Span
2
E,I
VL
VR
Load Nomenclature
W44x248
Span Data:
Span, L =
Inertia, I =
Full Uniform:
w=
Span #1
20.0000 ft
68.90 in.^4
Span #2
20.0000 ft
68.90 in.^4
1.0000 kpf
1.0000 kpf
Start
Distributed:
b (ft.)
wb (kips/ft.)
End
e (ft.)
we (kips/ft.)
Span #3
wb (kips/ft.)
Span #5
M's
ML:
MR:
Moment Matrix:
Dummy Span
a1
Start
b (ft.)
Span #4
End
e (ft.)
Start
we (kips/ft.)
b (ft.)
End
wb (kips/ft.)
e (ft.)
Start
we (kips/ft.)
b (ft.)
End
wb (kips/ft.)
e (ft.)
Start
we (kips/ft.)
b (ft.)
wb (kips/ft.)
End
e (ft.)
#1:
Ln/In:
we (kips/ft.)
b1
2*(Ln/In+L(n+1)/I(n+1))
Load Vector:
b1R
#2:
#3:
#4:
MnL+2*MnR, 2*MnL+MnR:
#5:
c1
#6:
###
#7:
W40x362
#8:
For 2 Spans:
###
a (ft.)
Point Loads:
P (kips)
a (ft.)
P (kips)
a (ft.)
P (kips)
a (ft.)
P (kips)
a (ft.)
P (kips)
###
#1:
###
#2:
pans:
#3:
###
#4:
###
#5:
###
#6:
#7:
1:
#8:
2:
#9:
3:
#10:
2:
#11:
#12:
M1 =
#13:
M2 =
#14:
M3 =
#15:
M1 =
M2 =
Moments:
c (ft.)
M (ft-kips)
c (ft.)
M (ft-kips)
c (ft.)
M (ft-kips)
c (ft.)
M (ft-kips)
c (ft.)
M (ft-kips)
M3 =
#1:
M4 =
#2:
M2 =
#3:
M3 =
#4:
M4 =
M5 =
0.00
kips
0.00
ft-kips
0.00
kips
0.00
ft-kips
M3 =
M4 =
7.50 k
-12.50 k
12.50 k
-7.50 k
---
---
---
---
---
---
M5 =
M6 =
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