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Nathaniel Gant ME 201 Statics Computer Project

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External Unknowns RA RB RC RD RE RFx RFy RJ

Given L= b= h= W=

12.5 7.25 17 750

ft ft ft lb

Member Unknowns BH GH

Brick Reaction Force Equations ∑MA = -W(X) + RB(L) RB = W(X) / L ∑FY = 0 = RA + RB - W RA = W - RB ∑MA = -W(X) - W(X-b) + RB(L) RB = [W(X) + W(X-b)] / L ∑FY = 0 = RA + RB - W - W RA = W + W - RB ∑MA = -W(X-b) + RB1(L) RB1 = W(X-b)/L ∑FY = 0 = RA + RB1 - W RA = W - RB1 ∑MB = -W(X-L) + RC(L) RC= W(X-L)/L ∑FY= 0= RB2 + RC-W RB2 = W - RC RB = RB1 + RB2 ∑MB = -W(X-L) - W(X-b-L) + RC(L) RC = [W(X-L) + W(X-b-L)] / L ∑FY = 0 = RB + RC- W - W RB = W + W - RC ∑MB = -W(X-b-L) + RC1(L) RC1 = W(X-b-L) / L ∑FY = 0 = RB + RC1 - W RB = W - RC1 ∑MC = -W(X-2L) + RD(L) RD = W(X-2L) / L ∑FY = 0 = RC2 + RD - W RC2 = W - RD RC= RC1 + RC2 ∑MC = -W(X-2L) - W(X-b-2L) + RD(L) RD = [W(X-2L) + W(X-b-2L)] / L ∑FY = 0 = RC + RD - W - W RC = W + W - RD ∑MC = -W(X-b-2L) + RD1(L) RD1 = W(X-b-2L) / L ∑FY = 0 = RC + RD1 - W RC = W - RD1 ∑MD = -W(X-3L) + RE(L) RE = W(X-3L) / L ∑FY = 0 = RD2 + RE - W RD2 = W - RE RD = RD1 + RD2 ∑MD = -W(X-3L) - W(X-b-3L) + RE(L) RE = [W(X-3L) + W(X-b-3L)] / L ∑FY = 0 = RD + RE - W - W RD = W + W - RE ∑MD = -W(X-b-3L) + RE(L) RE = W(X-b-3L) / L ∑FY = 0 = RD + RE - W RD = W - RE

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Max BH Compression using Solver x BH (C) (ft) (lb) -330.4781 12.500

Values External Equations ∑MJ= 0 = RA(50) + RB(37.5) + RC(25) + RD(12.5) - RFy(50) RFy = [RA(50) + RB(37.5) + RC(25) + RD(12.5)] / 50 ∑Fx = RFx = 0 ∑Fy = RA + RB + RC + RD + RE + RFy + RJ RJ = RA + RB + RC + RD + RE - RFy

x<b b<x<L L<x<L+b L+b<x<2L 2L<x<2L+b 2L+b<x<3L 3L<x<3L+b 3L+b<x<4L 4L<x<4L+b -

1065 435 -

*

Max BH Tension using Solver x BH (T) (ft) (lb) 795.9402 32.2500

Section Equations ∑MB = 0 = RA(L) - RFy(L) + GH(h) GH = [-RA(L) + RFy(L)] / h ∑MC = 0 = RA(2L) + RB(L) + GH(h) - RFy(2L) + (h / √h2 + L2)BH(L) BH= (√h2 + L2 / h*L)*(RFy(2L) - RA(2L) - RB(L) -GH(h))

X (ft) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 51 52 54 56

Force Vs Distance BH GH (lb) (lb) -37.23697 66.17647 -74.47393 132.35294 -111.71090 198.52941 -162.91173 289.52206 -237.38566 421.87500 -311.85960 554.22794 -274.62263 620.40441 -200.14870 664.52206 -125.67476 708.63971 -32.58235 741.72794 190.83945 697.61029 414.26126 653.49265 563.20912 609.37500 637.68306 565.25735 712.15699 521.13971 786.63092 477.02206 730.77547 432.90441 656.30154 388.78676 581.82761 344.66912 507.35367 300.55147 432.87974 256.43382 358.40581 212.31618 283.93187 168.19853 209.45794 124.08088 116.36552 68.93382 97.74704 57.90441 60.51007 35.84559 23.27310 13.78676

X=

RA RB RC RD RE RFx RFy RJ BH GH

X=

12.5 Unknowns 435 1065 0 0 0 0 1233.75 266.25 -330.47808 587.31618

19.75 Unknowns

RA RB RC RD RE RFx RFy RJ BH GH

0 1065 435 0 0 0 1016.25 483.75 -60.51007 747.24265

X=

32.25 Unknowns

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Max GH Tension using Solver x GH (ft) (lb) 19.7500 747.2426

RA RB RC RD RE RFx RFy RJ BH GH

0 0 1065 435 0 0 641.25 858.75 795.94017 471.50735

Statics on Excel  

This document is a pdf version of excel caluclations for determining loads on various beam members as a truck drives across a bridge.

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