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"MOVLOADS" --- MOVING WHEEL LOADS ANALYSIS
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Program Description:
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"MOVLOADS" is a spreadsheet program written in MS-Excel for the purpose of analysis of simple-span members
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subjected to from one (1) up to eight (8) moving wheel loads with up to seven (7) wheel spacings. Specifically,
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the maximum moment and location from the left end of the member and wheel postioning, the maximum end
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shears, the maximum deflection, and the maximum center support reaction for two (2) adjacent simple-span
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members are calculated.
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This program is a workbook consisting of two (2) worksheets, described as follows:
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Worksheet NameDescription
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DocThis documentation sheet
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Moving LoadsMoving loads analysis for single-span members
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Program Assumptions and Limitations:
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1. The following references were used in the development of this program (see below):
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a. "Modern Formulas for Statics and Dynamics, A Stress-and-Strain Approach"
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by Walter D. Pilkey and Pin Yu Chang, McGraw-Hill Book Company (1978), pages 11 to 21.
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b. AISC 9th Edition Allowable Stress (ASD) Manual (1989), pages 2-298 and 2-310.
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2. This program uses the three (3) following assumptions as a basis for analysis:
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a. Beams must be of constant cross section (E and I are constant for entire span length).
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b. Deflections must not significantly alter the geometry of the problem.
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c. Stress must remain within the "elastic" region.
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3. To determine the value of the maximum moment and location from the left end of the left span for either only one
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(1) or two (2) wheel loads, those values are calculated directly by formulas.
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4. To determine the value of the maximum moment and location from the left end of the left span for three (3) up to
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eight (8) wheel loads, the group of wheel loads is positioned with wheel load P1 situated directly over the left
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support. Then the group is moved to the right in 1/200*span increments, and the left and right reactions as well
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as the moments under each of the wheel loads are calculated. In moving the group of wheel loads incrementally
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from left to right, any wheels that would drop off of the span are done so. Then this entire procedure is mirrored
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for the opposite direction, from right to left.
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5. To determine the value of the maximum reaction at the center support of 2 adjacent simple spans, the group of
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wheels is positioned with the right most wheel load situated directly over the center support. Then the group is
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moved to the right, one wheel position at a time, until the left most wheel load, P1, is positioned directly over the
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center support. In moving the group of wheel loads one wheel position at a time from left to right, any wheels at
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either end that would drop off of the span(s) are done so.
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6. The calculated value for the maximum deflection is determined from dividing the beam into fifty (50) equal
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segments with fifty-one (51) points, and including all of the point load locations as well. (Note: the actual point of
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maximum deflection is where the slope = 0.)
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7. The user is given the ability to input two (2) specific locations from the left end of the beam to calculate the
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shear, moment, slope, and deflection.
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8. This program contains “comment boxes” which contain a wide variety of information including explanations of
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input or output items, equations used, data tables, etc. (Note: presence of a “comment box” is denoted by a
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“red triangle” in the upper right-hand corner of a cell. Merely move the mouse pointer to the desired cell to view
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the contents of that particular "comment box".)
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Formulas Used to Determine Shear, Moment, Slope, and Deflection in Single-Span Members
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For Uniform Load:
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Loading functions for uniform load evaluated at distance x = L from left end of beam:
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FvL =-w*L
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FmL =-w*L^2/2
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FqL =
-w*L^3/(6*E*I)
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FDL =
-w*L^4/(24*E*I)
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Loading functions for uniform load evaluated at distance = x from left end of beam:
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Fvx =-w*x
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Fmx =-w*x^2/2
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Fqx =
-w*x^3/(6*E*I)
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FDx =
-w*x^4/(24*E*I)
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For Point Loads:
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Loading functions for each point load evaluated at distance x = L from left end of beam:
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FvL =-P
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FmL =-P*(L-a)
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FqL =
-P*(L-a)^2/(2*E*I)
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FDL =
P*(L-a)^3/(6*E*I)
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Loading functions for each point load evaluated at distance = x from left end of beam:
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If x > a:
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Fvx =-Pelse:Fvx =0
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Fmx =-P*(x-a)else:Fmx =0
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Fqx =
-P*(x-a)^2/(2*E*I)
else:Fqx =0
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FDx =
P*(x-a)^3/(6*E*I)
else:FDx =0
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Initial summation values at left end (xL = 0) for shear, moment, slope, and deflection:
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Simple beam:
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Vo =-1/L*S(FmL)
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Mo =0
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qo =
1/L*S(FDL)+L/(6*E*I)*S(FmL)
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Do =
0
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Summations of shear, moment, slope, and deflection at distance = xL from left end of beam:
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Shear:Vx =Vo+S(Fvx)
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Moment:Mx =
Mo+Vo*x+S(Fmx)
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Slope:qx =
qo+Mo*x/(E*I)+Vo*x^2/(2*E*I)+S(Fqx)
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Deflection:Dx =
-(Do-qo*x-Mo*x^2/(2*E*I)-Vo*x^3/(6*E*I)+S(FDx)
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