P1 q1 P2W1

Q R S T

h1

q2 P1 q1W2

M N O P

h2

P2 q2 P1W3

I J K L

h3

q1 P2 q2W4

E F G H

h4

C D

h5

A B

L1 L2 L3

BALOK EI DIMENSI KOLOM EI DIMENSIQR 1 20/30 AE 2,5 40/50RS 1 20/30 EI 2 35/45ST 1 20/30 IM 1,5 25/35MN 1,5 25/35 MQ 1 20/20NO 1,5 25/35 BF 2,5 40/50OP 1,5 25/35 FJ 2 35/45IJ 2 35/45 JN 1,5 25/35JK 2 35/45 NR 1 20/20KL 2 35/45 CG 2,5 40/50EF 2,5 40/50 GK 2 35/45FG 2,5 40/50 KO 1,5 25/35GH 2,5 40/50 OS 1 20/20

DH 2,5 40/50HL 2 35/45LP 1,5 25/35PT 1 20/20

P1 = 1 ton   L1 = 5m  

P2 = 1,5 ton   L2

= 4,5 m  

q1 = 1t/m'   L3

= 5,5 m  

q2 = 2t/m'   h1 = 4m  

W1 = 5 ton   h2 = 4m  

W2 = 4 ton   h3 = 5m  

W3 = 3 ton   h4 = 5m  

W4 = 2,5 ton   h5 = 3m  

MOMEN PENGGOYANGAN / PERPUTARAN

SIKLUS I

A. PENGGOYANGAN

M”(IK) = D(IK) {∑C(IK) + Mo(IK) + M’(KI)}

M”(UQ) = –0,375 (10 + 0 + 0) = –3,750M”(VR) = –0,375 (10) = –3,750M”(WS) = –0,375 (10) = –3,750M”(XT) = –0,375 (10) = –3,750

M”(QM) = –0,375 (16,5 + 0 + 0) = –6,188M”(RN) = –0,375 (16,5) = –6,188M”(SO) = –0,375 (16,5) = –6,188M”(TP) = –0,375 (16,5) = –6,188

M”(MI) = –0,375 (20 + 0 + 0) = –7,500M”(NJ) = –0,375 (20) = –7,500M”(OK) = –0,375 (20) = –7,500M”(PL) = –0,375 (20) = –7,500

M”(IE) = –0,375 (30 + 0 + 0) = –11,250M”(JF) = –0,375 (30) = –11,250M”(KG) = –0,375 (30) = –11,250M”(LH) = –0,375 (30) = –11,250

M”(EA) = –0,375 (40 + 0 + 0) = –15,000M”(FB) = –0,375 (40) = –15,000M”(GC) = –0,375 (40) = –15,000M”(HD) = –0,375 (40) = –15,000

B. PERPUTARAN

Dimulai dari U–V–W–X–T–S–R–Q–M–N–O–P–L–K–J–I–E–F–G–H

M’(IK) = R(IK) {Mo(I) + M’(KI) + M’(IK)}

M’(UQ) = –0,082 (0,5 + 0 – 3,75) = 0,268M’(UV) = –0,418 (0,5 + 0 – 3,75) = 1,357

M’(VU) = –0,228 (0,5 + 1,357 + 0 + 0 – 3,75) = 0,431M’(VR) = –0,045 (0,5 + 1,357 + 0 + 0 – 3,75) = 0,085M’(VW) = –0,228 (0,5 + 1,357 + 0 + 0 – 3,75) = 0,431

M’(WV) = –0,268 (5 + 0,431 + 0 + 0 – 3,75) = –0,451M’(WS) = –0,053 (5 + 0,431 + 0 + 0 – 3,75) = –0,089M’(WX) = –0,179 (5 + 0,431 + 0 + 0 – 3,75) = –0,301

M’(XW) = –0,386 (–6 – 0,301 + 0 – 3,75) = 3,877M’(XT) = –0,114 (–6 – 0,301 + 0 – 3,75) = 1,149

M’(TX) = –0,035 (–6 + 1,149 + 0 – 3,75 – 6,188) = 0,521M’(TP) = –0,042 (–6 + 1,149 + 0 – 3,75 – 6,188) = 0,625M’(TS) = –0,423 (–6 + 1,149 + 0 – 3,75 – 6,188) = 6,249

M’(ST) = –0,186 (3,333 + 6,249 – 0,089 + 0 – 3,75 – 6,188) = 0,083M’(SW) = –0,016 (3,333 + 6,249 – 0,089 + 0 – 3,75 – 6,188) = 0,007M’(SO) = –0,019 (3,333 + 6,249 – 0,089 + 0 – 3,75 – 6,188) = 0,008M’(SR) = –0,280 (3,333 + 6,249 – 0,089 + 0 – 3,75 – 6,188) = 0,124

M’(RS) = –0,236 (1,167 + 0,124 + 0,085 + 0 – 3,75 – 6,188) = 2,017M’(RV) = –0,013 (1,167 + 0,124 + 0,085 + 0 – 3,75 – 6,188) = 0,112M’(RN) = –0,016 (1,167 + 0,124 + 0,085 + 0 – 3,75 – 6,188) = 0,134

M’(RQ) = –0,236 (1,167 + 0,124 + 0,085 + 0 – 3,75 – 6,188) = 2,017

M’(QR) = –0,446 (1,5 + 2,017 + 0,268 – 3,75 – 6,188) = 2,741M’(QU) = –0,025 (1,5 + 2,017 + 0,268 – 3,75 – 6,188) = 0,152M’(QM) = –0,030 (1,5 + 2,017 + 0,268 – 3,75 – 6,188) = 0,183

M’(MQ) = –0,022 (2 + 0,183 + 0 – 6,188 – 7,5) = 0,258M’(MI) = –0,142 (2 + 0,183 + 0 – 6,188 – 7,5) = 1,630M’(MN) = –0,336 (2 + 0,183 + 0 – 6,188 – 7,5) = 3,864

M’(NM) = –0,201 (2 + 3,864 + 0,134 + 0 – 6,188 – 7,5) = 1,545M’(NR) = –0,013 (2 + 3,864 + 0,134 + 0 – 6,188 – 7,5) = 0,103M’(NJ) = –0,085 (2 + 3,864 + 0,134 + 0 – 6,188 – 7,5) = 0,652M’(NO) = –0,201 (2 + 3,864 + 0,134 + 0 – 6,188 – 7,5) = 1,545

M’(ON) = –0,232 (5 + 1,545 + 0,008 + 0 – 6,188 – 7,5) = 1,655M’(OS) = –0,015 (5 + 1,545 + 0,008 + 0 – 6,188 – 7,5) = 0,110M’(OK) = –0,098 (5 + 1,545 + 0,008 + 0 – 6,188 – 7,5) = 0,698M’(OP) = –0,155 (5 + 1,545 + 0,008 + 0 – 6,188 – 7,5) = 1,103

M’(PO) = –0,289 (–9 + 1,103 + 0,625 – 6,188 – 7,5) = 6,048M’(PT) = –0,029 (–9 + 1,103 + 0,625 – 6,188 – 7,5) = 0,605M’(PL) = –0,183 (–9 + 1,103 + 0,625 – 6,188 – 7,5) = 3,827

M’(LP) = –0,063 (–3 + 3,827 – 7,5 – 11,25) = 1,131M’(LH) = –0,177 (–3 + 3,827 – 7,5 – 11,25) = 3,177M’(LK) = –0,260 (–3 + 3,827 – 7,5 – 11,25) = 4,654

M’(KL) = –0,146 (1,083 + 4,654 + 0,698 – 7,5 – 11,25) = 1,797M’(KO) = –0,035 (1,083 + 4,654 + 0,698 – 7,5 – 11,25) = 0,437M’(KG) = –0,100 (1,083 + 4,654 + 0,698 – 7,5 – 11,25) = 1,227M’(KJ) = –0,219 (1,083 + 4,654 + 0,698 – 7,5 – 11,25) = 2,696

M’(JK) = –0,191 (–1,083 + 2,696 + 0,652 – 7,5 – 11,25) = 3,150M’(JN) = –0,031 (–1,083 + 2,696 + 0,652 – 7,5 – 11,25) = 0,510M’(JF) = –0,087 (–1,083 + 2,696 + 0,652 – 7,5 – 11,25) = 1,433M’(JI) = –0,191 (–1,083 + 2,696 + 0,652 – 7,5 – 11,25) = 3,150

M’(IJ) = –0,309 (2,5 + 3,150 + 1,630 – 7,5 – 11,25) = 3,546M’(IM) = –0,050 (2,5 + 3,150 + 1,630 – 7,5 – 11,25) = 0,575M’(IE) = –0,141 (2,5 + 3,150 + 1,630 – 7,5 – 11,25) = 1,614

M’(EI) = –0,122 (2,5 + 1,614 + 0 – 11,25 – 15) = 2,701M’(EA) = –0,110 (2,5 + 1,614 + 0 – 11,25 – 15) = 2,431M’(EF) = –0,268 (2,5 + 1,614 + 0 – 11,25 – 15) = 5,935

M’(FE) = –0,175 (0,167 + 5,935 + 1,433 – 11,25 – 15) = 3,266M’(FJ) = –0,079 (0,167 + 5,935 + 1,433 – 11,25 – 15) = 1,487M’(FB) = –0,071 (0,167 + 5,935 + 1,433 – 11,25 – 15) = 1,338M’(FG) = –0,175 (0,167 + 5,935 + 1,433 – 11,25 – 15) = 3,266

M’(GF) = –0,198 (3,333 + 3,266 + 1,227 – 11,25 – 15) = 3,639M’(GK) = –0,090 (3,333 + 3,266 + 1,227 – 11,25 – 15) = 1,656M’(GC) = –0,081 (3,333 + 3,266 + 1,227 – 11,25 – 15) = 1,491M’(GH) = –0,132 (3,333 + 3,266 + 1,227 – 11,25 – 15) = 2,426

M’(HG) = –0,218 (–6 + 2,426 + 3,177 – 11,25 – 15) = 5,800M’(HL) = –0,149 (–6 + 2,426 + 3,177 – 11,25 – 15) = 3,960M’(HC) = –0,134 (–6 + 2,426 + 3,177 – 11,25 – 15) = 3,564

SIKLUS II

A. PENGGOYANGAN

M”(UQ) = –0,375{10+(0,268+0,183)+(0,085+0,134)+(–0,089+0,008)+(1,149+0,625)} = –4,636M”(VR) = –0,375 (12,363) = –4,636M”(WS) = –0,375 (12,363) = –4,636M”(XT) = –0,375 (12,363) = –4,636

M”(QM) = –0,375{16,5+(0,183+1,630)+(0,134+0,652)+(0,008+0,698)+(0,625+3,827)}= –9,097M”(RN) = –0,375 (24,258) = –9,097M”(SO) = –0,375 (24,258) = –9,097M”(TP) = –0,375 (24,258) = –9,097

M”(MI) = –0,375{20+(1,630+1,614)+(0,652+1,433)+(0,698+1,227)+(3,827+3,177)}= –12,847M”(NJ) = –0,375 (34,259) = –12,847M”(OK) = –0,375 (34,259) = –12,847M”(PL) = –0,375 (34,259) = –12,847

M”(IE) = –0,375{30+(1,614+2,431)+(1,433+1,338)+(1,227+1,491)+(3,177+3,564)}= –17,353M”(JF) = –0,375 (46,275) = –17,353M”(KG) = –0,375 (46,275) = –17,353M”(LH) = –0,375 (46,275) = –17,353

M”(EA) = –0,375 (40 + 2,431 + 1,338 + 1,491 + 3,564) = –18,309M”(FB) = –0,375 (48,823) = –18,309M”(GC) = –0,375 (48,823) = –18,309M”(HD) = –0,375 (48,823) = –18,309

B. PERPUTARAN

M’(UQ) = –0,082 (0,5 + 0,431 + 0,152 – 4,636) = 0,293M’(UV) = –0,418 (0,5 + 0,431 + 0,152 – 4,636) = 1,484

M’(VU) = –0,228 (0,5 + 1,484 – 0,451 + 0,112 – 4,636) = 0,681M’(VR) = –0,045 (0,5 + 1,484 – 0,451 + 0,112 – 4,636) = 0,134M’(VW) = –0,228 (0,5 + 1,484 – 0,451 + 0,112 – 4,636) = 0,681

M’(WV) = –0,268 (5 + 0,681 + 3,877 + 0,007 – 4,636) = –1,322M’(WS) = –0,053 (5 + 0,681 + 3,877 + 0,007 – 4,636) = –0,261M’(WX) = –0,179 (5 + 0,681 + 3,877 + 0,007 – 4,636) = –0,881

M’(XW) = –0,386 (–6 – 0,881 + 0,521 – 4,636) = 4,242M’(XT) = –0,114 (–6 – 0,881 + 0,521 – 4,636) = 1,257

M’(TX) = –0,035 (–6 + 1,257 + 0,083 – 0,605 – 4,636 – 9,097) = 0,626M’(TP) = –0,042 (–6 + 1,257 + 0,083 – 0,605 – 4,636 – 9,097) = 0,752M’(TS) = –0,423 (–6 + 1,257 + 0,083 – 0,605 – 4,636 – 9,097) = 7,516

M’(ST) = –0,186 (3,333 + 7,516 + 2,017 – 0,261 + 0,110 – 4,636 – 9,097) = 0,189M’(SW) = –0,016 (3,333 + 7,516 + 2,017 – 0,261 + 0,110 – 4,636 – 9,097) = 0,016M’(SO) = –0,019 (3,333 + 7,516 + 2,017 – 0,261 + 0,110 – 4,636 – 9,097) = 0,019M’(SR) = –0,280 (3,333 + 7,516 + 2,017 – 0,261 + 0,110 – 4,636 – 9,097) = 0,284

M’(RS) = –0,236 (1,167 + 0,284 + 0,134 + 2,741 + 0,103 – 4,636 – 9,097) = 2,192M’(RV) = –0,013 (1,167 + 0,284 + 0,134 + 2,741 + 0,103 – 4,636 – 9,097) = 0,122M’(RN) = –0,016 (1,167 + 0,284 + 0,134 + 2,741 + 0,103 – 4,636 – 9,097) = 0,146M’(RQ) = –0,236 (1,167 + 0,284 + 0,134 + 2,741 + 0,103 – 4,636 – 9,097) = 2,192

M’(QR) = –0,446 (1,5 + 2,192 + 0,293 + 0,258 – 4,636 – 9,097) = 4,228M’(QU) = –0,025 (1,5 + 2,192 + 0,293 + 0,258 – 4,636 – 9,097) = 0,235M’(QM) = –0,030 (1,5 + 2,192 + 0,293 + 0,258 – 4,636 – 9,097) = 0,282

M’(MQ) = –0,022 (2 + 0,282 + 1,545 + 0,575 – 9,097 – 12,847) = 0,393M’(MI) = –0,142 (2 + 0,282 + 1,545 + 0,575 – 9,097 – 12,847) = 2,486M’(MN) = –0,336 (2 + 0,282 + 1,545 + 0,575 – 9,097 – 12,847) = 5,893

M’(NM) = –0,201 (2 + 5,893 + 0,146 + 1,655 + 0,510 – 9,097 – 12,847) = 2,359M’(NR) = –0,013 (2 + 5,893 + 0,146 + 1,655 + 0,510 – 9,097 – 12,847) = 0,157M’(NJ) = –0,085 (2 + 5,893 + 0,146 + 1,655 + 0,510 – 9,097 – 12,847) = 0,995M’(NO) = –0,201 (2 + 5,893 + 0,146 + 1,655 + 0,510 – 9,097 – 12,847) = 2,359

M’(ON) = –0,232 (5 + 2,359 + 0,019 + 6,048 + 0,437 – 9,097 – 12,847) = 1,875M’(OS) = –0,015 (5 + 2,359 + 0,019 + 6,048 + 0,437 – 9,097 – 12,847) = 0,125M’(OK) = –0,098 (5 + 2,359 + 0,019 + 6,048 + 0,437 – 9,097 – 12,847) = 0,791M’(OP) = –0,155 (5 + 2,359 + 0,019 + 6,048 + 0,437 – 9,097 – 12,847) = 1,250

M’(PO) = –0,289 (–9 + 1,250 + 0,752 + 1,131 – 9,097 – 12,847) = 8,025M’(PT) = –0,029 (–9 + 1,250 + 0,752 + 1,131 – 9,097 – 12,847) = 0,802M’(PL) = –0,183 (–9 + 1,250 + 0,752 + 1,131 – 9,097 – 12,847) = 5,078

M’(LP) = –0,063 (–3 + 5,078 + 3,960 + 1,797 – 12,847 – 17,353) = 1,411M’(LH) = –0,177 (–3 + 5,078 + 3,960 + 1,797 – 12,847 – 17,353) = 3,964M’(LK) = –0,260 (–3 + 5,078 + 3,960 + 1,797 – 12,847 – 17,353) = 5,807

M’(KL) = –0,146 (1,083 + 5,807 + 0,791 + 1,656 + 3,150 – 12,847 – 17,353) = 2,585M’(KO) = –0,035 (1,083 + 5,807 + 0,791 + 1,656 + 3,150 – 12,847 – 17,353) = 0,628M’(KG) = –0,100 (1,083 + 5,807 + 0,791 + 1,656 + 3,150 – 12,847 – 17,353) = 1,765M’(KJ) = –0,219 (1,083 + 5,807 + 0,791 + 1,656 + 3,150 – 12,847 – 17,353) = 3,878

M’(JK) = –0,191 (–1,083 + 3,878 + 0,995 + 1,487 + 3,546 – 12,847 – 17,353) = 4,084M’(JN) = –0,031 (–1,083 + 3,878 + 0,995 + 1,487 + 3,546 – 12,847 – 17,353) = 0,662M’(JF) = –0,087 (–1,083 + 3,878 + 0,995 + 1,487 + 3,546 – 12,847 – 17,353) = 1,859M’(JI) = –0,191 (–1,083 + 3,878 + 0,995 + 1,487 + 3,546 – 12,847 – 17,353) = 4,084

M’(IJ) = –0,309 (2,5 + 4,084 + 2,486 + 2,701 – 12,847 – 17,353) = 5,698M’(IM) = –0,050 (2,5 + 4,084 + 2,486 + 2,701 – 12,847 – 17,353) = 0,923M’(IE) = –0,141 (2,5 + 4,084 + 2,486 + 2,701 – 12,847 – 17,353) = 2,593

M’(EI) = –0,122 (2,5 + 2,593 + 3,266 – 17,353 – 18,309) = 3,332M’(EA) = –0,110 (2,5 + 2,593 + 3,266 – 17,353 – 18,309) = 2,999M’(EF) = –0,268 (2,5 + 2,593 + 3,266 – 17,353 – 18,309) = 7,321

M’(FE) = –0,175 (0,167 + 7,321 + 1,859 + 3,639 – 17,353 – 18,309) = 3,958M’(FJ) = –0,079 (0,167 + 7,321 + 1,859 + 3,639 – 17,353 – 18,309) = 1,801M’(FB) = –0,071 (0,167 + 7,321 + 1,859 + 3,639 – 17,353 – 18,309) = 1,621M’(FG) = –0,175 (0,167 + 7,321 + 1,859 + 3,639 – 17,353 – 18,309) = 3,958

M’(GF) = –0,198 (3,333 + 3,958 + 1,765 + 5,8 – 17,353 – 18,309) = 4,109M’(GK) = –0,090 (3,333 + 3,958 + 1,765 + 5,8 – 17,353 – 18,309) = 1,870M’(GC) = –0,081 (3,333 + 3,958 + 1,765 + 5,8 – 17,353 – 18,309) = 1,683M’(GH) = –0,132 (3,333 + 3,958 + 1,765 + 5,8 – 17,353 – 18,309) = 2,740

M’(HG) = –0,218 (–6 + 2,740 + 3,964 – 17,353 – 18,309) = 7,609M’(HL) = –0,149 (–6 + 2,740 + 3,964 – 17,353 – 18,309) = 5,195M’(HC) = –0,134 (–6 + 2,740 + 3,964 – 17,353 – 18,309) = 4,675

∑MV = 0 Q1 = 1.4 = 4Ru.4 – P2.2 – Q1.2 – Muv + Mvu = 0Ru.4 – 1,5.2 – 4.2 – 1,79 + 1,96 = 0 q1Ru.4 – 10,83 = 0

RU RV

X1 X2P2

Muv Mvu

Ru = 2,707

∑MU = 0– Rv.4 + P2.2 + Q1.2 – Muv + Mvu = 0– Rv.4 + 1,5.2 + 4.2 – 1,79 + 1,96 = 0– Rv.4 + 11,17 = 0Rv = 2,793

∑V = 0Ru + Rv – P2 – Q1 = 0 2,707 + 2,793 – 1,5 - 4 = 0 ( OKE!!!!!!! ) - 1,96 - 1,626

- 1,79 - 1,376

MOMEN MMX1 = Ru.X1 – ½ q1.x²- Muv 0 X1 2Xu = 0 ; Mu = 2,707.0 – ½ .1.0² - 1,79 = - 1,79Xo = 2 ; Mo = 1,207.2 – ½.1.2² - 1,79 = - 1,376

MX2 = Rv.X2 – ½.q1.x² - Mvu 0 X2 2Xv = 0 ; Mv = 2,793.0 – ½.1.0² - 1,96 = - 1,96Xo = 2 ; Mo = 2,793.2 – ½.1.2² - 1,96 = - 1,626

LINTANG 1,207QX1 = Ru – q1.x1 0 X1 2Xu = 0 ; Qu = 1,207 – 1.0 = 1,207 0,707 Xo = 2 ; Qo = 1,207 – 1.2 = - 0,793

QX2 = – Rv + q1.x2 0 X2 2 QXv = 0 ; Qv = - 1,293 + 1.0 = - 1,293 -0,793Xo = 2 ; Qo = - 1,293 + 1.2 = 0,707

- 1,293

Q1 = 1.4 = 4∑MW = 0Rv.4 – P2.2 – Q1.2 – Mvw + Mwv = 0Rv.4 – 1,5.2 – 4.2 – 1,15 + 0,55 = 0 q1Rv.4 – 11,6 = 0

22

RV RW

X1 X2

P2 = 1,5

Mvw Mwv

Rv = 2,9

∑MV = 0– Rw.4 + P2.2 + Q1.2 – Mvw + Mwv = 0– Rw.4 + 1,5.2 + 4.2 – 1,15 + 0,55 = 0– Rw.4 + 10,4 = 0 Rw = 2,6

∑V = 0Rv + Rw - P2 - Q1 = 0 2,9 + 2,6 – 1,5 - 4 = 0 ( OKE!!!!!!!! ) - 1,15

- 0,55

MOMEN MMX1 = Rv.X1 – ½.q1.x² -Mvw 0 X1 2Xv = 0 ; Mv = 2,9.0 – ½.1.0² - 1,15 = – 1,15Xo = 2 ; Mo = 2,9.2 – ½.1.2² - 1,15 = 2,65

2,65MX2 = Rw.X2 – ½.q1.x² -Mwv 0 X2 2Xw = 0 ; Mw = 2,6.0 – ½.1.0² - 0,55 = – 0,55Xo = 2 ; Mo = 2,6.2 – ½.1.2² - 0,55 = 2,65

LINTANG 2,9QX1 = Rv – q1.x1 0 X1 2Xv = 0 ; Qv = 2,9 – 1.0 = 2,9Xo = 2 ; Qo = 2,9 – 1.2 = 0,9

0,9QX2 = – Rw + q1.x2 0 X2 2 QXw = 0 ; Qw = – 2,6 + 1.0 = - 2,6 - 0,6Xo = 2 ; Qo = – 2,6 + 1.2 = - 0,6

- 2,6

∑MX = 0Rw.5 – P1.2,5 – Mwx + Mxw = 0Rw.5 – 1.2,5 – 2,22 + 0,72 = 0Rw.5 – 4 = 0Rw = 0,8

22

RW RX

X1 X2P1

Mwx Mxw

2,52,5

∑MW = 0– Rx.5 + P1.2,5 – Mwx + Mxw = 0– Rx.5 + 1.2,5 – 2,22 + 0,72 = 0– Rx.5 + 1 = 0Rx = 0,2

- 2,22∑V = 0Rw + Rx – P1 = 0 0,8 + 0,2 – 1 = 0 ( OKE!!!!!!!! )

- 0,22 - 0,72

MOMEN MMX1 = Rw.X1 – Mwx 0 X1 2,5Xw = 0 ; Mw = 0,8.0 – 2,22 = - 2,22X○ = 2,5; M○ = 0,8.2,5 – 2,22 = - 0,22

MX2 = Rx.X2 – Mxw 0 X2 2,5Xx = 0 ; Mx = 0,2.0 – 0,72 = - 0,72X○ = 2,5 ; M○ = 0,2.2,5 – 0,72 = - 0,22

LINTANG 0,8 0,8QX1 = Rw 0 X1 2,5Xw = 0 ; Qw = 0,8 QX○ = 2,5; Q○ = 0,8

- 0,2 - 0,2QX2 = – Rx + q1.X2 0 X2 2,5Xx = 0 ; Qx = – 0,2Xc = 2,5;Q○ = – 0,2

∑MR = 0Rq.4 – P3.2 – Mqr + Mrq = 0Rq.4 – 2.2 – 2,56 + 0,77 = 0Rq.4 – 5,79 = 0Rq = 1,45

∑MQ = 0

RQ RR

X1 X2

P3 = 2

Mqr Mrq

22

– Rr.4 + P3.2 – Mqr + Mrq = 0– Rr.4 + 2.2 – 2,56 + 0,77 = 0– Rr.4 + 2,21 = 0Rr = 0,55

∑V = 0 - 2,56Rq + Rr – P3 = 01,45 + 0,55 – 2 = 0 ( OKE!!!!!!!! )

- 0,77

MOMEN MMX1 = Rq.X1 – Mqr 0 X1 2 0,33Xq = 0 ; Mq = 1,45.0 – 2,56 = – 2,56 0,34Xo = 2 ; Mo = 1,45.2 – 2,56 = 0,34

MX2 = Rr.X2 – Mrq 0 X2 2Xr = 0 ; Mr = 0,55.0 – 0,77 = –0,77Xo = 2 ; Mo = 0,55.2 – 0,77 = 0,33

LINTANGQX1 = Rq 0 X1 2 1,45 1,45Xq = 0 ; Qq = 1,45Xo = 2 ; Qo = 1,45 Q

QX2 = – Rr 0 X2 2 - 0,55 - 0,55Xr = 0 ; Qr = – 0,55Xo = 2 ; Qo = – 0,55

∑MS = 0Rr.4 – P4.2 – Mrs + Msr = 0Rr.4 – 1,5.2 – 1,10 + 1,32 = 0Rr.4 – 2,78 = 0Rr = 0,695

∑MR = 0– Rs.4 + P4.2 – Mrs + Msr = 0

RR RS

X1 X2 P4= 1,5

Mrs Msr

22

– Rs.4 + 1,5.2 – 1,10 + 1,32 = 0– Rs.4 + 3,22 = 0Rs = 0,805

∑V = 0 - 1,32Rr + Rs – P4 = 0 - 1,1 0,695 + 0,805 – 1,5 = 0 ( OKE!!!!!!! )

MMOMEN 0,29MX1 = Rr.X1 – Mrs 0 X1 2Xr = 0 ; Mr = 0,695.0 – 1,1 = – 1,1X○ = 2 ; M○ = 0,695.2 – 1,10 = 0,29

MX2 = Rs.X2 – Msr 0 X2 2Xs = 0 ; Ms = 0,805.0 – 1,32 = – 1,32X○ = 2 ; M○ = 0,805.2 – 1,32 = 0,29

LINTANG QX1 = Rr 0 X1 2 0,695 0,695Xr = 0 ; Qr = 0,695 Xb = 2 ; Qb = 0,695 Q

QX2 = – Rs 0 X2 2 - 0,805 - 0,805Xs = 0 ; Qs = – 0,805 Xb = 2 ; Qb = – 0,805

∑MT = 0 P5 = 1 Q2=2.2,5 Rs.5–Q2.1,25-P5.2,5– Mst + Mts = 0 = 5Rs.5 – 5.1,25–1.2,5-6,66+0,35 = 0 Rs.5 – 15,06 = 0Rs = 3,012

∑MS = 0– Rt.5 + Q2.3,75 + P5.2,5 – Mst + Mts = 0– Rt.5 + 5.3,75 + 1.2,5 – 6,66+ 0,35 = 0

RS RT

X1 X2q2 = 2

Mst Mts

2,52,5

– Rt.5 + 14,94 = 0Rt = 2,988

∑V = 0Rs + Rt – Q2 - P5 = 0 - 6,66 -5,383,012 – 2,988 – 5 - 1 = 0 ( OKE!!!!!!! ) - 0,35

MOMEN 0,87 MMX1 = Rs.X1 – ½ q2.X1

2 – Mst 0 X1 2,5Xs = 0 ; Ms = 3,012.0 – ½ 2.02 – 6,66 = – 6,66X○ = 2,5 ; M○ = 3,012.2,5 – ½ 2.2,52 – 6,66 = - 5,38

MX2 = Rt.X2 – ½ q2.X22 – Mts 0 X2 2,5

Xt = 0 ; Mt = 2,988.0 – ½ 2.02 – 0,35 = – 0,35X○ = 2,5 ; M○ = 2,988.2,5 – ½ 2.2,52 – 0,35 = 0,87

LINTANG 3,012 2,012QX1 = Rs – q2.X1 0 X1 2,5Xs = 0 ; Qs = 3,012 – 2.0 = 3,012 QX○ = 2,5 ;Q○ = 3,012 – 2.2,5 = - 1,988 - 1,988 - 2,988 QX2 = – Rt + q2.X2 0 X2 2,5Xt = 0 ; Qt = – 2,988 + 2.0 = – 2,988X○ = 2,5 ; Q○ = – 2,988 + 2.2,5 = 2,012

∑MN = 0Rm.4 – P1.2 – Mmn + Mnm = 0Rm.4 – 1.2 – 2,54+1,38 = 0Rm.4 – 3,16 = 0Rm = 0,79

∑MM = 0– Rn.4 + P1.2 – Mmn + Mnm = 0– Rn.4 + 1.2 – 2,54 + 1,38 = 0– Rn.4 + 0,84 = 0

RM RN

X1 X2

P1 = 1

Mmn Mnm

22

Rn = 0,21

∑V = 0Rm + Rn – P1 = 0 0,79+0,21–1 = 0 ( OKE !!!!! ) -2,54 -1,38

- 0,96

MOMEN MMX1 = Rm.X1 – Mmn 0 X1 2Xm = 0; Mm = 0,79.0 – 2,54 = – 2,54Xo = 2 ; Mo = 0,79.2 – 2,54 = - 0,96

MX2 = Rn.X2 – Mnm 0 X2 2Xn = 0 ; Mn = 0,21.0 – 1,38 = – 1,38Xo = 2 ; Mo = 0,21.2 – 1,38 = - 0,96

LINTANGQX1 = Rm 0 X1 2 0,79 0,79Xm = 0; Qm = 0,79Xo = 2 ; Qo = 0,79 Q

-0,21 - 0,21MX2 = – Rn 0 X2 2Xn = 0 ; Qn = – 0,21Xo = 2 ; Qo = – 0,21

∑MO = 0Rn.4 – P2.2 – Mno + Mon = 0Rn.4 – 1,5.2 – 2,79 + 1,59 = 0Rn.4 – 4,2 = 0Rn = 1,05

∑MN = 0– Ro.4 + P2.2 – Mno + Mon = 0– Ro.4 + 1,5.2 – 2,79+1,59 = 0– Ro.4 + 1,8 = 0Ro = 0,45

RN RO

X1 X2 P2 = 1,5

Mno Mon

22

∑V = 0Rn + Ro – P2 = 0 - 2,79 1,05 + 0,45– 1,5 = 0 ( OKE !!!!! )

- 1,59- 0,69

MOMEN MMX1 = Rn.X1 – Mno 0 X1 2Xn = 0 ; Mn = 1,05.0 – 2,79 = – 2,79X○ = 2 ; M○ = 1,05.2 – 2,79 = - 0,69

MX2 = Ro.X2 – Mon 0 X2 2Xn = 0 ; Mn = 0,45.0 – 1,59 = – 1,59Xo = 2 ; Mo = 0,45.2 – 1,59 = - 0,69

LINTANGQX1 = Rn 0 X1 2 1,05 1,05Xn = 0 ; Qn = 1,05 Xb = 2 ; Qb = 1,05 Q

QX2 = – Ro 0 X2 2 -0,45 -0,45Xo = 0 ; Qo = – 0,45Xb = 2 ; Qb = – 0,45

∑MO = 0Ro.5 – P3.2,5 – Mop + Mpo = 0Ro.5 – 2.2,5 – 3,93 + 2,12 = 0Ro.5 – 6,81 = 0Ro = 1,362

∑MP = 0– Rp.5 + P3.2,5 – Mop + Mpo = 0– Rp.5 + 2.2,5 – 3,93 + 2,12 = 0– Rp.5 + 3,19 = 0Rp = 0,638

RO RP

X1 X2 P3 = 2

Mop Mpo

2,52,5

∑V = 0Ro + Rp – P3 = 0 1,362 + 0,638 – 2 = 0 ( OKE !!!!! ) - 3,93

- 2,12- 0,525

MOMEN MMX1 = Ro.X1 – Mop 0 X1 2,5Xo = 0 ; Mo = 1,362.0 – 3,93 = – 3,93Xp = 2,5 ; Mp = 1,362.2,5 – 3,93 = - 0,525

MX2 = Rp.X2 – Mpo 0 X2 2,5Xp= 0 ; Mp = 0,638.0 – 2,12 = – 2,12Xo = 2,5 ; Mo = 0,638.2,5 – 2,12 = - 0,525

LINTANG 1,362 1,362QX1 = Ro 0 X1 2,5Xo = 0 ; Qo = 1,362 QXp = 2,5; Qp = 1,362 - 0,638 -0,638

QX2 = – Rp 0 X2 2,5Xp = 0 ; Qp = – 0,638 Xc = 2,5; Qc = – 0,638

∑MJ = 0 Q3 = 3.4 = 12Ri.4 – Q3.2 – Mij + Mji = 0 q3=3Ri.4 – 12.2 – 6,79 + 0,61 = 0Ri.4 – 30,18 = 0Ri = 7,545

∑MI = 0– Rj.4 + Q3.2 – Mij + Mji = 0– Rj.4 + 12.2 – 6,79+0,61 = 0– Rj.4 + 17,82 = 0Rj = 4,455 - 6,79

∑V = 0

RI RJ

X1 X2

Mij Mji

22

Ri + Rj – Q3 = 0 7,545 + 4,455 – 12 = 0 ( OKE!!!!!!! )

- 0,61MOMEN MMX1 = Ri.X1 – ½ q3.x²– Mij 0 X1 2Xi = 0 ; Mi = 7,545.0 – ½.3.0² - 6,79 = – 6,79Xo = 2 ; Mo = 7,545.2 – ½.3.2² - 6,79 = 2,3 2,3

MX2 = Rj.X2 – ½.q3.x²– Mji 0 X2 2 7,545Xj = 0 ; Mj = 4,455.0 – ½.3.0² - 0,61 = – 0,61Xo = 2 ; Mo = 4,455.2 – ½.3.2² - 0,61 = 2,3

LINTANGQX1 = Ri – q3.x 0 X1 2 1,545Xi = 0 ; Qi = 7,545 – 3.0 = 7,545Xo = 2 ; Qo =7,545 – 3.2 = 1,545

QQX2 = – Rj + q3.x 0 X2 2Xj = 0 ; Qj = – 4,455 + 3.0 = - 4,455Xo = 2 ; Qo = –4,455 + 3.2 = 1,545

- 4,455

∑MK = 0Rj.4 – Q3.2 – Mjk + Mkj = 0 Q3=3.4=12Rj.4 – 12.2 – 6,04+2,19 = 0Rj.4 – 27,85 = 0Rj = 6,963

∑MJ = 0– Rk.4 + Q3.2 – Mjk + Mkj = 0– Rk.4 + 12.2 – 6,04 + 2,19 = 0– Rk.4 + 20,15 = 0Rk = 5,037

- 6,04∑V = 0Rj + Rk – Q3 = 0

RJ RK

X1 X2

Mjk Mkj

22

q3 = 3

6,963+5,037 – 12 = 0 ( OKE!!!!!! )- 2,19

MOMENMX1 = Rj.X1 – ½.q3.x² – Mjk 0 X1 2 MXj = 0 ; Mj = 6,963.0 – ½.3.0² - 6,04 = – 6,04 1,88Xo = 2 ; Mo = 6,963.2 – ½.3.2² - 6,04 = 1,88

MX2 = Rk.X2 – ½ q3. x2 – Mkj 0 X2 2 6,963Xk = 0 ; Mk = 5,037.0 – ½ 3.02 – 2,19 = – 2,19Xo = 2 ; Mo = 5,037.2 – ½ 3.22 – 2,19 = 1,88

LINTANGQX1 = Rj – q3.x 0 X1 2Xj = 0 ; Qj = 6,963 – 3.0 = 6,963Xo = 2 ; Qo = 6,963 – 3.2 = 0,963 0,963

QQX2 = – Rk + q3.X2 0 X2 2Xk = 0 ; Qk = – 5,037 + 3.0 = - 5,037Xo = 2 ; Qo = – 5,037 + 3.2 = 0,963

- 5,037

∑ML = 0Rk.5 –Q3.2,5 – Mkl + Mlk = 0 Q3 = 3.5 = 15Rk.5 – 15.2,5 – 9,44 + 1,15 = 0Rk.5 – 45,79 = 0Rk = 9,158

∑MK = 0– Rl.5 + Q3.2,5 – Mkl + Mlk = 0 - 9,44– Rl.5 + 15.2,5 – 9,44 + 1,15 = 0– Rl.5 + 29,21 = 0Rl = 5,842

∑V = 0Rk + Rl – Q3 = 0 9,158 + 5,842 – 15 = 0 ( OKE!!!!!!! )

RK RL

X1 X2

q3 = 3

Mkl Mlk

2,52,5

- 1,15MOMENMX1 = Rk.X1 – ½ q3.X1

2 – Mkl 0 X1 2,5 MXk = 0 ; Mk = 9,158.0 – ½.3.02 – 9,44 = – 9,44Xo = 2,5 ;Mo = 9,158.2,5 – ½ .3.2,52 – 9,44 = 4,08

MX2 = Rl.X2 – ½ q3.X22 – Mlk 0 X2 2,5

Xl= 0 ; Ml = 5,842 .0 – ½ 3.02 – 1,15 = – 1,15 9,158Xo = 2,5 ; Mo = 5,842.2,5 – ½ 3.2,52 – 1,15 = 4,08 4,08

LINTANGQX1 = Rk – q3.X1 0 X1 3Xk = 0 ; Qk = 9,158 – 3.0 = 9,158Xo = 2,5 ; Qo = 9,158 – 3.2,5 = 1,658

QX2 = – Rl + q3.X2 0 X2 3 1,658Xl = 0 ; Ql = – 5,842 + 3.0 = – 5,842Xo = 2,5 ; Qo = – 5,842 + 3.2,5 = 1,658 Q

- 5,842

∑MF = 0Re.4 –Q4.2 – Mef + Mfe = 0 Q4=1.4= 4Re.4 – 4.2 –10,96+7,36= 0 q4 = 1Re.4 – 11,6 = 0Re = 2,9

∑ME = 0 -10,96– Rf.4 + Q4.2 – Mef + Mfe = 0– Rf.4 + 4.2 – 10,96 + 7,36 = 0– Rf.4 + 4,4 = 0Rf = 1,1 - 7,16 - 7,36

∑V = 0Re + Rf – Q4 = 0 - 6,16 2,9 + 1,1 – 4 = 0 ( OKE!!!!!!! )

RE RF

X1 X2 QQ

Mef Mfe

22

MOMEN MMX1 = Re.X1 – ½.q.x² - Mef 0 X1 2Xe = 0 ; Me = 2,9.0 – ½.1.0² - 10,96 = – 10,96Xo = 2 ; Mo = 2,9.2 – ½.1.2 – 10,96 = - 6,16

MX2 = Rf.X2 –1/2.q.x²- Mfe 0 X2 2Xf = 0 ; Mf = 1,1.0 – ½.1.0² - 7,36 = –7,36Xo = 2 ; Mo = 1,1.2 – ½.1.2² - 7,36 = - 7,16

LINTANG 2,9QX1 = Re – q4.x 0 X1 2Xe = 0 ; Qe = 2,9 – 1.0 = 2,9 0,9Xo = 2 ; Qo = 2,9 – 1.2 = 0,9

QQX2 = – Rf + q4.x 0 X2 2 - 1,1Xf = 0 ; Qf = – 1,1 + 1.0 = - 1,1Xo = 2 ; Qo = – 1,1 + 1.2 = 0,9

∑MG = 0 Q4 = 1.4 = 4Rf.4 – Q4.2 – Mfg + Mgf = 0Rf.4 – 4.2 – 8,24 + 6,08 = 0Rf.4 – 10,16 = 0Rf = 2,54

∑MF = 0 - 8,24– Rg.4 + Q4.2 – Mfg + Mgf = 0– Rg.4 + 4.2 – 8,24 + 6,08 = 0– Rg.4 + 5,84 = 0 - 6,08Rg = 1,46 - 5,16

∑V = 0Rf + Rg – Q4 = 0 2,54+1,46 – 4 = 0 ( OKE !!!!!! )

RF RG

X1 X2 q4=1

Mfg Mgf

22

MOMEN MMX1 = Rf.X1 – ½ q4.X1

2 – Mfg 0 X1 2Xf = 0 ; Mf = 2,54.0 – ½ 1.02 – 8,24 = – 8,24Xo = 2 ; Mo = 2,54.2 – ½ 1.22 – 8,24 = - 5,16

MX2 = Rg.X2 – ½ q4.X22 – Mgf 0 X2 2

Xg = 0 ; Mg = 1,46.0 – ½ 1.02 – 6,08 = –6,08 2,54Xo = 2 ; Mo = 1,46.2 – ½ 1.22 – 6,08 = - 5,16

LINTANG 0,54QX1 = Rf – q4.X1 0 X1 2 QXf = 0 ; Qf = 2,54 – 1.0 = 2,54Xb = 2 ; Qb = 2,54 – 1.2 = 0,54

- 1,46QX2 = – Rg + q4.X2 0 X2 2Xg = 0 ; Qg = – 1,46+ 1.0 = – 1,46Xb = 2 ; Qb = – 1,46 + 1.2 = 0,54

∑MH = 0Rg.5 – P1.2,5 – Mgh + Mhg = 0Rg.5 – 1.2,5 – 9,02 + 9,83 = 0Rg.5 – 1,69 = 0Rg = 0,338

∑MG = 0 - 9,83– Rh.5 + P1.2,5 – Mgh + Mhg = 0 -9,02– Rh.5 + 1.2,5 – 9,02 + 9,83 = 0– Rh.5 + 3,31 = 0 - 8,175Rh = 0,662

∑V = 0Rg + Rh – P1 = 0 0,338 + 0,662 – 1 = 0 ( OKE !!!!!!! )

MOMEN

RG RH

X1 X2 P1=1

Mgh Mhg

2,52,5

MX1 = Rg.X1 – Mgh 0 X1 2,5 MXg = 0 ; Mg = 0,338.0 – 9,02 = – 9,02Xo = 2,5 ; Mo = 0,338.2,5 – 9,02 = -8,175

MX2 = Rh.X2 – Mhg 0 X2 2,5Xh = 0 ; Mh = 0,662.0 – 9,83 = – 9,83Xo = 2,5 ; Mo = 0,662.2,5 – 9,83 = -8,175

LINTANGQX1 = Rg 0 X1 2,5Xg = 0 ; Qg = 0,338 0,338 0,338Xo = 2,5 ; Qo = 0,338

QQX2 = – Rh 0 X2 2,5Xh = 0 ; Qh = – 0,662 - 0,662 - 0,662Xo = 2,5 ; Qo = – 0,662

∑MQ = 0Ru.6 – Muq + Mqu = 0Ru.6 – + = 0Ru.6 = 0Ru =

∑MU = 0– Rq.6 – Muq + Mqu = 0– Rq.6 – + = 0– Rq.6 = 0Rq =

∑V = 0Ru + Rq = 0 + = 0

MOMENMX1 = Ru.X1 – Muq 0 X1 3

RU RQ

X1 X2

Muq Mqu

33

Xu = 0 ; Mu = .0 – = –Xo = 3 ; Mo = .3 – =

MX2 = Rq.X2 – Mqu 0 X2 3Xq = 0 ; Mq = .0 – = –Xo = 3 ; Mo = .3 – =

LINTANGQX1 = Ru 0 X1 3Xu = 0 ; Qu =Xo = 3 ; Qo =

MX2 = – Rq 0 X2 3Xq = 0 ; Qq = –Xo = 3 ; Qo = –

∑MR = 0Rv.6 – Mrv + Mvr = 0Rv.6 – + = 0Rv.6 = 0Rv =

∑MV = 0– Rr.6 – Mrv + Mvr = 0– Rr.6 – + = 0– Rr.6 = 0Rr =

∑V = 0Rv + Rr = 0 + = 0

MOMENMX1 = Rv.X1 – Mvr 0 X1 3Xv = 0 ; Mv = .0 – = –

RV RR

X1 X2

Mvr Mrv

33

Xo = 3 ; Mo = .3 – =

MX2 = Rr.X2 – Mrv 0 X2 3Xr = 0 ; Mr = .0 – = –Xo = 3 ; Mo = .3 – =

LINTANGQX1 = Rv 0 X1 3Xv = 0 ; Qv =Xo = 3 ; Qo =

MX2 = – Rr 0 X2 3Xr = 0 ; Qr = –Xo = 3 ; Qo = –

∑MS = 0Rw.6 – Mws + Msw = 0Rw.6 – + = 0Rw.6 = 0Rw =

∑MW = 0– Rs.6 – Mws + Msw = 0– Rs.6 – + = 0– Rs.6 = 0Rs =

∑V = 0Rw + Rs = 0 + = 0

MOMENMX1 = Rw.X1 – Mws 0 X1 3Xw = 0 ; Mw = .0 – = –Xo = 3 ; Mo = .3 – =

RW RS

X1 X2

Mws Msw

33

MX2 = Rs.X2 – Msw 0 X2 3Xs = 0 ; Ms = .0 – = –Xo = 3 ; Mo = .3 – =

LINTANGQX1 = Rw 0 X1 3Xw = 0 ; Qw =Xo = 3 ; Qo =

MX2 = – Rs 0 X2 3Xs = 0 ; Qs = –Xo = 3 ; Qo = –

∑MT = 0Rx.6 – Mxt + Mtx = 0Rx.6 – + = 0Rx.6 = 0Rx =

∑MX = 0– Rt.6 – Mxt + Mtx = 0– Rt.6 – + = 0– Rt.6 = 0Rt =

∑V = 0Rx + Rt = 0 + = 0

MOMENMX1 = Rx.X1 – Mxt 0 X1 3Xx = 0 ; Mx = .0 – = –Xo = 3 ; Mo = .3 – =

RX RT

X1 X2

Mxt Mtx

33

MX2 = Rt.X2 – Mtx 0 X2 3Xt = 0 ; Mt = .0 – = –Xo = 3 ; Mo = .3 – =

LINTANGQX1 = Rx 0 X1 3Xx = 0 ; Qx =Xo = 3 ; Qo =

MX2 = – Rt 0 X2 3Xt = 0 ; Qt = –Xo = 3 ; Qo = –

∑MM = 0Rq.5 – Mqm + Mmq = 0Rq.5 – + = 0Rq.5 = 0Rq =

∑MQ = 0– Rm.5 – Mqm + Mmq = 0– Rm.5 – + = 0– Rm.5 = 0Rm =

∑V = 0Rq + Rm = 0 + = 0

MOMENMX1 = Rq.X1 – Mqm 0 X1 2,5Xq = 0 ; Mq = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Rm.X2 – Mmq 0 X2 2,5

RQ RM

X1 X2

Mqm Mmq

2,52,5

Xm = 0 ; Mm = .0 – = –Xo = 2,5; Mo = .2,5 – =

LINTANGQX1 = Rq 0 X1 2,5Xq = 0 ; Qq =Xo = 2,5; Qo =

MX2 = – Rm 0 X2 2,5Xm = 0 ; Qm = –Xo = 2,5; Qo = –

∑MN = 0Rr.5 – Mrn + Mnr = 0Rr.5 – + = 0Rr.5 = 0Rr =

∑MR = 0– Rn.5 – Mrn + Mnr = 0– Rn.5 – + = 0– Rn.5 = 0Rn =

∑V = 0Rr + Rn = 0 + = 0

MOMENMX1 = Rr.X1 – Mrn 0 X1 2,5Xr = 0 ; Mr = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Rn.X2 – Mnr 0 X2 2,5Xn = 0 ; Mn = .0 – = –

RR RN

X1 X2

Mrn Mnr

2,52,5

Xo = 2,5; Mo = .2,5 – =

LINTANGQX1 = Rr 0 X1 2,5Xr = 0 ; Qr =Xo = 2,5; Qo =

MX2 = – Rn 0 X2 2,5Xn = 0 ; Qn = –Xo = 2,5; Qo = –

∑MO = 0Rs.5 – Mso + Mos = 0Rs.5 – + = 0Rs.5 = 0Rs =

∑MS = 0– Ro.5 – Mso + Mos = 0– Ro.5 – + = 0– Ro.5 = 0Ro =

∑V = 0Rs + Ro = 0 + = 0

MOMENMX1 = Rs.X1 – Mso 0 X1 2,5Xs = 0 ; Ms = .0 – = –Xa = 2,5 ;Ma = .2,5 – =

MX2 = Ro.X2 – Mos 0 X2 2,5Xo = 0 ; Mo = .0 – = –Xa = 2,5; Ma = .2,5 – =

RS RO

X1 X2

Mso Mos

2,52,5

LINTANGQX1 = Rs 0 X1 2,5Xs = 0 ; Qs =Xa = 2,5; Qa =

MX2 = – Ro 0 X2 2,5Xo = 0 ; Qo = –Xa = 2,5; Qa = –

∑MP = 0Rt.5 – Mtp + Mpt = 0Rt.5 – + = 0Rt.5 = 0Rt =

∑MT = 0– Rp.5 – Mtp + Mpt = 0– Rp.5 – + = 0– Rp.5 = 0Rp =

∑V = 0Rt + Rp = 0 + = 0

MOMENMX1 = Rt.X1 – Mtp 0 X1 2,5Xt = 0 ; Mt = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Rp.X2 – Mpt 0 X2 2,5Xp = 0 ; Mp = .0 – = –Xo = 2,5; Mo = .2,5 – =

RT RP

X1 X2

Mtp Mpt

2,52,5

LINTANGQX1 = Rt 0 X1 2,5Xt = 0 ; Qt =Xo = 2,5; Qo =

MX2 = – Rp 0 X2 2,5Xp = 0 ; Qp = –Xo = 2,5; Qo = –

∑MI = 0Rm.4 – Mmi + Mim = 0Rm.4 – + = 0Rm.4 = 0Rm =

∑MM = 0– Ri.4 – Mmi + Mim = 0– Ri.4 – + = 0– Ri.4 = 0Ri =

∑V = 0Rm + Ri = 0 + = 0

MOMENMX1 = Rm.X1 – Mmi 0 X1 2Xm = 0; Mm = .0 – = –Xo = 2 ; Mo = .2 – =

MX2 = Ri.X2 – Mim 0 X2 2Xi = 0 ; Mi = .0 – = –Xo = 2 ; Mo = .2 – =

RM RI

X1 X2

Mmi Mim

22

LINTANGQX1 = Rm 0 X1 2Xm = 0; Qm =Xo = 2 ; Qo =

MX2 = – Ri 0 X2 2Xi = 0 ; Qi = –Xo = 2 ; Qo = –

∑MJ = 0Rn.4 – Mnj + Mjn = 0Rn.4 – + = 0Rn.4 = 0Rn =

∑MN = 0– Rj.4 – Mnj + Mjn = 0– Rj.4 – + = 0– Rj.4 = 0Ri =

∑V = 0Rn + Rj = 0 + = 0

MOMENMX1 = Rn.X1 – Mnj 0 X1 2Xn = 0 ; Mn = .0 – = –Xo = 2 ; Mo = .2 – =

MX2 = Rj.X2 – Mjn 0 X2 2Xj = 0 ; Mj = .0 – = –Xo = 2 ; Mo = .2 – =

LINTANG

RN RJ

X1 X2

Mnj Mjn

22

QX1 = Rn 0 X1 2Xn = 0 ; Qn =Xo = 2 ; Qo =

MX2 = – Rj 0 X2 2Xj = 0 ; Qj = –Xo = 2 ; Qo = –

∑MK = 0Ro.4 – Mok + Mko = 0Ro.4 – + = 0Ro.4 = 0Ro =

∑MO = 0– Rk.4 – Mok + Mko = 0– Rk.4 – + = 0– Rk.4 = 0Rk =

∑V = 0Ro + Rk = 0 + = 0

MOMENMX1 = Ro.X1 – Mok 0 X1 2Xo = 0 ; Mo = .0 – = –Xa = 2 ; Ma = .2 – =

MX2 = Rk.X2 – Mko 0 X2 2Xk = 0 ; Mk = .0 – = –Xa = 2 ; Ma = .2 – =

LINTANGQX1 = Ro 0 X1 2

RO RK

X1 X2

Mok Mko

22

Xo = 0 ; Qo =Xa = 2 ; Qa =

MX2 = – Rk 0 X2 2Xk = 0 ; Qk = –Xa = 2 ; Qa = –

∑ML = 0Rp.4 – Mpl + Mlp = 0Rp.4 – + = 0Rp.4 = 0Rp =

∑MP = 0– Rl.4 – Mpl + Mlp = 0– Rl.4 – + = 0– Rl.4 = 0Rl =

∑V = 0Rp + Rl = 0 + = 0

MOMENMX1 = Rp.X1 – Mpl 0 X1 2Xp = 0 ; Mp = .0 – = –Xo = 2 ; Mo = .2 – =

MX2 = Rl.X2 – Mlp 0 X2 2Xl = 0 ; Ml = .0 – = –Xo = 2 ; Mo = .2 – =

LINTANGQX1 = Rp 0 X1 2Xp = 0 ; Qp =

RP RL

X1 X2

Mpl Mlp

22

Xo = 2 ; Qo =

MX2 = – Rl 0 X2 2Xl = 0 ; Ql = –Xo = 2 ; Qo = –

∑ME = 0Ri.4,5 – Mie + Mei = 0Ri.4,5 – + = 0Ri.4,5 = 0Ri =

∑MI = 0– Re.4,5 – Mie + Mei = 0– Re.4,5 – + = 0– Re.4,5 = 0Re =

∑V = 0Ri + Re = 0 + = 0

MOMENMX1 = Ri.X1 – Mie 0 X1 2,25Xi = 0 ; Mi = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

MX2 = Re.X2 – Mei 0 X2 2,25Xe = 0 ; Me = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

LINTANGQX1 = Ri 0 X1 2,25Xi = 0 ; Qi =Xo = 2,25 ; Qo =

RI RE

X1 X2

Mie Mei

2,252,25

MX2 = – Re 0 X2 2,25Xe = 0 ; Qe = –Xo = 2,25 ; Qo = –

∑MF = 0Rj.4,5 – Mjf + Mfj = 0Rj.4,5 – + = 0Rj.4,5 = 0Rj =

∑MJ = 0– Rf.4,5 – Mjf + Mfj = 0– Rf.4,5 – + = 0– Rf.4,5 = 0Rf =

∑V = 0Rj + Rf = 0 + = 0

MOMENMX1 = Rj.X1 – Mjf 0 X1 2,25Xj = 0 ; Mj = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

MX2 = Rf.X2 – Mfj 0 X2 2,25Xf = 0 ; Mf = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

LINTANGQX1 = Rj 0 X1 2,25Xj = 0 ; Qj =Xo = 2,25 ; Qo =

RJ RF

X1 X2

Mjf Mfj

2,252,25

MX2 = – Rf 0 X2 2,25Xf = 0 ; Qf = –Xo = 2,25 ; Qo = –

∑MG = 0Rk.4,5 – Mkg + Mgk = 0Rk.4,5 – + = 0Rk.4,5 = 0Rk =

∑MK = 0– Rg.4,5 – Mkg + Mgk = 0– Rg.4,5 – + = 0– Rg.4,5 = 0Rg =

∑V = 0Rk + Rg = 0 + = 0

MOMENMX1 = Rk.X1 – Mkg 0 X1 2,25Xk = 0 ; Mk = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

MX2 = Rg.X2 – Mgk 0 X2 2,25Xg = 0 ; Mg = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

LINTANGQX1 = Rk 0 X1 2,25Xk = 0 ; Qk =Xo = 2,25 ; Qo =

MX2 = – Rg 0 X2 2,25

RK RG

X1 X2

Mkg Mgk

2,252,25

Xg = 0 ; Qg = –Xo = 2,25 ; Qo = –

∑MH = 0Rj.4,5 – Mjh + Mhj = 0Rj.4,5 – + = 0Rj.4,5 = 0Rj =

∑MJ = 0– Rh.4,5 – Mjh + Mhj = 0– Rh.4,5 – + = 0– Rh.4,5 = 0Rh =

∑V = 0Rj + Rh = 0 + = 0

MOMENMX1 = Rj.X1 – Mjh 0 X1 2,25Xj = 0 ; Mj = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

MX2 = Rh.X2 – Mhj 0 X2 2,25Xh = 0 ; Mh = .0 – = –Xo = 2,25 ; Mo = .2,25 – =

LINTANGQX1 = Rj 0 X1 2,25Xj = 0 ; Qj =Xo = 2,25 ; Qo =

MX2 = – Rh 0 X2 2,25Xh = 0 ; Qh = –

RJ RH

X1 X2

Mjh Mhj

2,252,25

Xo = 2,25 ; Qo = –

∑MA = 0Re.5 – Mea + Mae = 0Re.5 – + = 0Re.5 = 0Re =

∑ME = 0– Ra.5 – Mea + Mae = 0– Ra.5 – + = 0– Ra.5 = 0Ra =

∑V = 0Re + Ra = 0 + = 0

MOMENMX1 = Re.X1 – Mea 0 X1 2,5Xe = 0 ; Me = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Ra.X2 – Mae 0 X2 2,5Xa = 0 ; Ma = .0 – = –Xo = 2,5; Mo = .2,5 – =

LINTANGQX1 = Re 0 X1 2,5Xe = 0 ; Qe =Xo = 2,5; Qo =

MX2 = – Ra 0 X2 2,5Xa = 0 ; Qa = –Xo = 2,5; Qo = –

RE RA

X1 X2

Mea Mae

2,52,5

∑MB = 0Rf.5 – Mfb + Mbf = 0Rf.5 – + = 0Rf.5 = 0Rf =

∑MF = 0– Rb.5 – Mfb + Mbf = 0– Rb.5 – + = 0– Rb.5 = 0Rb =

∑V = 0Rf + Rb = 0 + = 0

MOMENMX1 = Rf.X1 – Mfb 0 X1 2,5Xf = 0 ; Mf = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Rb.X2 – Mbf 0 X2 2,5Xb = 0 ; Mb = .0 – = –Xo = 2,5; Mo = .2,5 – =

LINTANGQX1 = Rf 0 X1 2,5Xf = 0 ; Qf =Xo = 2,5; Qo =

MX2 = – Rb 0 X2 2,5Xb = 0 ; Qb = –Xo = 2,5; Qo = –

RF RB

X1 X2

Mfb Mbf

2,52,5

∑MC = 0Rg.5 – Mgc + Mcg = 0Rg.5 – + = 0Rg.5 = 0Rg =

∑MG = 0– Rc.5 – Mgc + Mcg = 0– Rc.5 – + = 0– Rc.5 = 0Rc =

∑V = 0Rg + Rc = 0 + = 0

MOMENMX1 = Rg.X1 – Mgc 0 X1 2,5Xg = 0 ; Mg = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Rc.X2 – Mcg 0 X2 2,5Xc = 0 ; Mc = .0 – = –Xo = 2,5; Mo = .2,5 – =

LINTANGQX1 = Rg 0 X1 2,5Xg = 0 ; Qg =Xo = 2,5; Qo =

MX2 = – Rc 0 X2 2,5Xc = 0 ; Qc = –Xo = 2,5; Qo = –

RG RC

X1 X2

Mgc Mcg

2,52,5

∑MD = 0Rh.5 – Mhd + Mdh = 0Rh.5 – + = 0Rh.5 = 0Rh =

∑MH = 0– Rn.5 – Mhd + Mdh = 0– Rn.5 – + = 0– Rn.5 = 0Rn =

∑V = 0Rh + Rd = 0 + = 0

MOMENMX1 = Rh.X1 – Mhd 0 X1 2,5Xh = 0 ; Mh = .0 – = –Xo = 2,5 ;Mo = .2,5 – =

MX2 = Rd.X2 – Mdh 0 X2 2,5Xd = 0 ; Md = .0 – = –Xo = 2,5; Mo = .2,5 – =

LINTANGQX1 = Rh 0 X1 2,5Xh = 0 ; Qh =Xo = 2,5; Qo =

MX2 = – Rd 0 X2 2,5Xd = 0 ; Qd = –Xo = 2,5; Qo = –

RH RD

X1 X2

Mhd Mdh

2,52,5