2/2/2019
Problem 001-ms | Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 001-ms | Method of Sections
Problem 001-ms
From the truss in Fig. T-01, determine the force in mebers BC, CE, and EF.
Solution 001-ms
Click here to show or hide the solution
ΣMA = 0
3RD = 50(2) + 80(0.75)
RD = 53.33 kN
From the FBD of the section through a-a
ΣME = 0
0.75FBC + 2RD = 0.75(80) + 1(50)
https://www.mathalino.com/reviewer/engineering-mechanics/problem-001-ms-method-sections
1/4
2/2/2019
Problem 001-ms | Method of Sections | Engineering Mechanics Review
0.75FBC + 2(53.33) = 60 + 50
FBC = 4.45 kN tension
answer
ΣMC = 0
0.75FEF = 1(RD )
0.75FEF = 53.33
answer
FEF = 71.11 kN tension
ΣFV = 0
3
5
3
5
FC E + 50 = RD
FC E + 50 = 53.33
FC E = 5.55 kN tension
Tags: Truss
Truss member
answer
Method of Sections
‹ Method of Sections | Analysis of Simple
Trusses
Subscribe to MATHalino.com on
Custom Search
YouTube
up
Problem 002-ms | Method of Sections ›
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-001-ms-method-sections
2/4
2/2/2019
Problem 001-ms | Method of Sections | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
Problem 418 - Warren Truss by Method of Sections
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-001-ms-method-sections
3/4
2/2/2019
Problem 001-ms | Method of Sections | Engineering Mechanics Review
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-001-ms-method-sections
4/4
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 002-mj | Method of Joints
Problem 002-mj
The structure in Fig. T-02 is a truss which is pinned to the floor at point A, and supported by a roller at point
D. Determine the force to all members of the truss.
Solution 002-mj
Click here to show or hide the solution
ΣMD = 0
6RA = 5(12) + 3(20)
RA = 20 kN
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
1/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
ΣMA = 0
6RD = 1(12) + 3(20)
RD = 12 kN
At joint A
ΣFV = 0
√21
5
√21
5
FAG = RA
FAG = 20
FAG = 21.82 kN compression
ΣFH = 0
FAB =
FAB =
2
5
2
5
FAG
(21.82)
FAB = 8.73 kN tension
At joint G
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
2/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
ΣFV = 0
√21
5
√21
5
FBG + 12 =
FBG + 12 =
√21
5
√21
5
FAG
(21.82)
FBG = 8.73 kN tension
ΣFH = 0
FF G =
FF G =
2
5
2
5
FAG +
2
5
FBG
(21.82) +
2
5
(8.73)
FF G = 12.22 kN compression
At joint B
ΣFV = 0
√21
5
FBF =
√21
5
FBG
FBF = FBG
FBF = 8.73 kN compression
ΣFH = 0
FBC = FAB +
FBC = 8.73 +
2
5
2
5
FBG +
2
5
(8.73) +
FBF
2
5
(8.73)
FBC = 15.71 kN tension
At joint F
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
3/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
ΣFV = 0
√21
5
√21
5
FC F +
FC F +
√21
5
√21
5
FBF = 20
(8.73) = 20
FC F = 13.09 kN compression
ΣFH = 0
FEF +
FEF +
2
5
2
5
FC F =
2
5
FBF + FF G
(13.09) =
2
5
(8.73) + 12.22
FEF = 10.48 kN compression
At joint C
ΣFV = 0
√21
5
FC E =
√21
5
FC F
FC E = FC F
FC E = 13.09 kN tension
ΣFH = 0
FC D +
FC D +
2
5
2
5
FC E +
2
5
FC F = FBC
(13.09) +
2
5
(13.09) = 15.71
FC D = 5.24 kN tension
At joint E
ΣFV = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
4/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
√21
5
FDE =
√21
5
FC E
FDE = FC E
FDE = 13.09 kN compression
ΣFH = 0
2
FEF =
FC E +
5
2
10.48 =
5
2
5
FDE
(13.09) +
2
5
(13.09)
check
10.5 = 10.5
At joint D
ΣFV = 0
√21
RD =
12 =
5
√21
FDE
(13.09)
5
check
12 = 12
ΣFH = 0
FC D =
5.24 =
2
5
2
5
FDE
(13.09)
5.24 = 5.24
check
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
5/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
Summary
FAB = 8.73 kN tension
FAG = 21.82 kN compression
FBC = 15.71 kN tension
FBF = 8.73 kN compression
FBG = 8.73 kN tension
FCD = 5.24 kN tension
FCE = 13.09 kN tension
FCF = 13.09 kN compression
FDE = 13.09 kN compression
FEF = 10.48 kN compression
FFG = 12.22 kN compression
Download Form (Free)
DOWNLOAD
To View Form, Download Now Search Forms Online
Tags: Truss
Truss Reaction
Method of Joints
‹ Problem 001-mj | Method of Joints
Warren Truss
up
Problem 003-mj | Method of Joints ›
Comments
How come that the hypotenuse
Permalink Submitted by leyst on May 15, 2017 - 6:51am.
How come that the hypotenuse in the solution became 5m where it is 2.5m?
What is shown in the solution
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
6/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
Permalink Submitted by Jhun Vert on May 15, 2017 - 9:47am.
What is shown in the solution is slope. 1/2.5 = 2/5. If you are not used in solving with slope, go with
angles.
Got it. Thank you
Permalink Submitted by leyst on May 18, 2017 - 6:58am.
Got it. Thank you
I dont get how you used the
Permalink Submitted by Daniel Siingwa on October 15, 2017 - 4:25am.
Great
how to find slope triangle
Permalink Submitted by rakshit on May 24, 2018 - 11:01pm.
how to find slope triangle please help
Use your scientific
Permalink Submitted by Jhun Vert on May 25, 2018 - 3:21pm.
Use your scientific calculator that is capable of displaying fraction. If you input 1/2.5 the calculator will
output 2/5.
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
7/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
Monetize your site
With ads you can count on
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
8/9
2/2/2019
Problem 002-mj | Method of Joints | Engineering Mechanics Review
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Study a top-ranked MBA
Online.
Internationally accredited.
ENROL NOW
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-mj-method-joints
9/9
2/2/2019
Problem 002-ms | Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 002-ms | Method of Sections
Problem 002-ms
The roof truss shown in Fig. T-03 is pinned at point A, and supported by a roller at point H. Determine the
force in member DG.
Solution 002-ms
Click here to show or hide the solution
ΣMA = 0
8RH = 2(55) + 4(90) + 6(45)
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-ms-method-sections
1/4
2/2/2019
Problem 002-ms | Method of Sections | Engineering Mechanics Review
RH = 92.5 kN
From section to the right of a-a
x + 2
x + 4
=
1.5
2.5
2.5x + 5 = 1.5x + 6
x = 1 m
ΣMO = 0
(x + 2) (
(1 + 2) (
5
√41
5
√41
15
√41
15
√41
FDG ) + xRH = (x + 2)(45)
FDG ) + 1(92.5) = (1 + 2)(45)
FDG + 92.5 = 135
FDG = 42.5
FDG = 18.14 kN tension
Tags: Truss
Truss member
answer
Truss Reaction
‹ Problem 001-ms | Method of Sections
roof truss
Method of Sections
up
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-ms-method-sections
Problem 003-ms | Method of Sections ›
2/4
2/2/2019
Problem 002-ms | Method of Sections | Engineering Mechanics Review
Get the USA
Products You Want
Sign Up Today for a MyUS Address. Fast
& Reliable Shipping to Your Home
OPEN
MyUs.com
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-ms-method-sections
3/4
2/2/2019
Problem 002-ms | Method of Sections | Engineering Mechanics Review
Problem 418 - Warren Truss by Method of Sections
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-002-ms-method-sections
4/4
2/2/2019
Problem 003-mj | Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 003-mj | Method of Joints
Problem 003-mj
Find the force in each member of the truss shown in Fig. T-04.
Solution 003-mj
Click here to show or hide the solution
At joint C
ΣFV = 0
5
√29
FC D = 80
FC D = 86.16 kN tension
ΣFH = 0
FBC =
FBC =
2
√29
2
√29
FC D
(86.16)
FBC = 32 kN compression
At joint D
ΣFV = 0
5
√29
FBD =
5
√29
FC D
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-mj-method-joints
1/5
2/2/2019
Problem 003-mj | Method of Joints | Engineering Mechanics Review
FBD = FC D
FBD = 86.16 kN compression
ΣFH = 0
FDE =
FDE =
2
FC D +
√29
2
2
√29
(86.16) +
√29
FBD
2
√29
(86.16)
FDE = 64 kN tension
At joint B
ΣFV = 0
5
√29
5
√29
5
FBE =
FBD + 60
√29
5
FBE =
(86.16) + 60
√29
FBE = 150.78 kN tension
ΣFH = 0
2
FAB = FBC +
√29
2
FAB = 32 +
FBD +
2
√29
2
(86.16) +
√29
FBE
(150.78)
√29
FAB = 120 kN compression
At joint E
ΣFV = 0
5
√29
5
FAE =
√29
FBE
FAE = FBE
FAE = 150.78 kN compression
ΣFH = 0
2
FEF = FDE +
FEF = 64 +
√29
2
√29
FBE +
2
√29
(150.78) +
FAE
2
√29
(150.78)
FEF = 176 kN tension
At joint A
ΣFV = 0
FAF =
FAF =
5
√29
5
√29
FAE
(150.78)
FAF = 140 kN tension
ΣFH = 0
RA = FAB +
RA = 120 +
2
√29
2
√29
FAE
(150.78)
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-mj-method-joints
2/5
2/2/2019
Problem 003-mj | Method of Joints | Engineering Mechanics Review
RA = 176 kN to the left
At joint F
ΣFH = 0
FH = FEF
FH = 176 kN to the right
ΣFV = 0
FV = FAF
FV = 140 kN upward
Checking
ΣMF = 0
5RA = 8(80) + 4(60)
RA = 176 kN to the left
check
ΣFH = 0
FH = RA
FH = 176 kN to the right
check
ΣFV = 0
FV = 80 + 60
FV = 140 kN upward
check
Summary
Top chords
FDE = 64 kN tension
FEF = 176 kN tension
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-mj-method-joints
3/5
2/2/2019
Problem 003-mj | Method of Joints | Engineering Mechanics Review
Bottom chords
FAB = 120 kN compression
FBC = 32 kN compression
Web members
FAF = 140 kN tension
FAE = 150.78 kN compression
FBE = 150.78 kN tension
FBD = 86.16 kN compression
FCD = 86.16 kN tension
Tags: Truss
Truss member
cantilever truss
‹ Problem 002-mj | Method of Joints
Truss Reaction
up
Method of Joints
Problem 004-mj | Method of Joints ›
Simple Event Creation
Platform
You're free to explore the tools until you
make the whole thing happen. It's free to
use!
Conferize
OPEN
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-mj-method-joints
4/5
2/2/2019
Problem 003-mj | Method of Joints | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Like us on Facebook
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-mj-method-joints
5/5
2/2/2019
Problem 003-ms | Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 003-ms | Method of Sections
Problem 003-ms
The truss in Fig. T-04 is pinned to the wall at point F, and supported by a roller at point C. Calculate the
force (tension or compression) in members BC, BE, and DE.
Figure T-04
Solution 003-ms
Click here to show or hide the solution
From section to the left of a-a
ΣFV = 0
5
√29
FBE = 80 + 60
FBE = 150.78 kN tension
answer
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-ms-method-sections
1/4
2/2/2019
Problem 003-ms | Method of Sections | Engineering Mechanics Review
ΣME = 0
5FBC = 6(80) + 2(60)
answer
FBC = 120 kN compression
ΣMB = 0
5FDE = 4(80)
answer
FDE = 64 kN tension
Tags: Truss
Truss member
cantilever truss
‹ Problem 002-ms | Method of Sections
Method of Sections
up
Problem 004-ms | Method of Sections ›
Get the USA
Products You Want
Sign Up Today for a MyUS Address. Fast
& Reliable Shipping to Your Home
MyUs.com
OPEN
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-ms-method-sections
2/4
2/2/2019
Problem 003-ms | Method of Sections | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
Problem 418 - Warren Truss by Method of Sections
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-ms-method-sections
3/4
2/2/2019
Problem 003-ms | Method of Sections | Engineering Mechanics Review
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-003-ms-method-sections
4/4
2/2/2019
Problem 004-mj | Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 004-mj | Method of Joints
Problem 004-mj
The truss pinned to the floor at D, and supported by a roller at point A is loaded as shown in Fig. T-06.
Determine the force in member CG.
Solution 004-mj
Click here to show or hide the solution
ΣMD = 0
6RA = 4(100) + 2(120)
RA = 106.67 kN
At joint F
FF G = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-mj-method-joints
1/4
2/2/2019
Problem 004-mj | Method of Joints | Engineering Mechanics Review
At joint A
ΣFV = 0
3
√13
3
√13
FAG = RA
FAG = 106.67
FAG = 128.20 kN compression
ΣFH = 0
FAB =
FAB =
2
√13
2
FAG
(128.20)
√13
FAB = 71.11 kN tension
At joint B
ΣFH = 0
FBC = FAB
FBC = 71.11 kN tension
ΣFV = 0
FBG = 0
At joint G
ΣFV = 0
3
√13
3
√13
FC G + 100 =
FC G + 100 =
3
√13
3
FAG
(128.20)
√13
FC G = 8.01 kN tension
answer
Another Solution to 004-mj
Click here to show or hide the solution
Tags: Truss
Truss member
Truss Reaction
‹ Problem 003-mj | Method of Joints
Method of Joints
up
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-mj-method-joints
Problem 005-mj | Method of Joints ›
2/4
2/2/2019
Problem 004-mj | Method of Joints | Engineering Mechanics Review
FEA for Dummies
The intro before the intro
We know FEA. Get the knowledge you
need from NAFEMS.
OPEN
nafems.org
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
Find The Best
Tenant
blueground
100% Occupancy Guaranteed. Enlist Your
Property For Review Today!
OPEN
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-mj-method-joints
3/4
2/2/2019
Problem 004-mj | Method of Joints | Engineering Mechanics Review
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Like us on Facebook
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-mj-method-joints
4/4
2/2/2019
Problem 004-ms | Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 004-ms | Method of Sections
Problem 004-ms
For the truss shown in Fig. T-05, find the internal fore in member BE.
Solution 003-ms
Click here to show or hide the solution
ΣMF = 0
6RA = 2(120)
RA = 40 kN
From section to the left of a-a
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-ms-method-sections
1/4
2/2/2019
Problem 004-ms | Method of Sections | Engineering Mechanics Review
ΣMA = 0
answer
FBE = 0
Tags: Truss
Truss Reaction
roof truss
Method of Sections
‹ Problem 003-ms | Method of Sections
up
Zero Stress
Problem 005-ms | Method of Sections ›
Rebar detailing
Software for rebar detailing in CAD systems
OPEN
Addosoft (PTY) LTD
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-ms-method-sections
2/4
2/2/2019
Problem 004-ms | Method of Sections | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
Problem 418 - Warren Truss by Method of Sections
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-ms-method-sections
3/4
2/2/2019
Problem 004-ms | Method of Sections | Engineering Mechanics Review
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Like us on Facebook
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-004-ms-method-sections
4/4
2/2/2019
Problem 005-mj | Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 005-mj | Method of Joints
Problem 005-mj
Compute the force in all members of the truss shown in Fig. T-08.
Solution 005-mj
Click here to show or hide the solution
ΣMF = 0
11RA = 7(50) + 3(30)
RA = 40 kN
ΣMA = 0
11RF = 4(50) + 8(30)
RF = 40 kN
At joint A
ΣFV = 0
5
√41
FAB = RA
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints-0
1/5
2/2/2019
Problem 005-mj | Method of Joints | Engineering Mechanics Review
5
√41
FAB = 40
FAB = 51.22 kN compression
ΣFH = 0
FAC =
FAC =
4
√41
4
FAB
(51.22)
√41
FAC = 32 kN tension
At joint B
ΣFH = 0
4
√17
4
√17
4
FBD =
√41
4
FBD =
FAB
(51.22)
√41
FBD = 32.98 kN compression
ΣFV = 0
FBC +
FBC +
5
√41
5
√41
FAB +
1
√17
(51.22) +
FBD = 50
1
√17
(32.98) = 50
FBC = 2 kN compression
At joint C
ΣFV = 0
1
√2
1
√2
FC D = FBC
FC D = 2
FC D = 2.83 kN tension
ΣFH = 0
FC E +
FC E +
1
√2
1
√2
FC D = FAC
(2.83) = 32
FC E = 30 kN tension
At joint E
ΣFH = 0
FEF = FC E
FEF = 30 kN tension
ΣFV = 0
FDE = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints-0
2/5
2/2/2019
Problem 005-mj | Method of Joints | Engineering Mechanics Review
At joint D
ΣFH = 0
3
5
3
5
1
FDF +
√2
1
FDF +
√2
FC D =
4
√17
FBD
4
(2.83) =
√17
(32.98)
FDF = 50 kN compression
ΣFV = 0
4
5
4
5
1
FDF =
FBD +
√17
1
(50) =
1
√2
(32.98) +
√17
FC D + 30
1
(2.83) + 30
√2
check
40 = 40
At joint F
ΣFV = 0
4
5
4
5
FDF = RA
(50) = 40
check
40 = 40
ΣFH = 0
FEF =
FEF =
3
5
3
5
FDF
(50)
30 = 30
check
Summary
Tags:
Truss Truss member
Truss Analysis
Truss Reaction
‹ Problem 004-mj | Method of Joints
Method of Joints
example of method of joints
up
Problem 403 | Method of Joints ›
Comments
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints-0
3/5
2/2/2019
Problem 005-mj | Method of Joints | Engineering Mechanics Review
How did you get the fractions
Permalink Submitted by Brian Berdin Molina on October 9, 2016 - 3:47pm.
How did you get the fractions?
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints-0
4/5
2/2/2019
Problem 005-mj | Method of Joints | Engineering Mechanics Review
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Like us on Facebook
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints-0
5/5
2/2/2019
Problem 005-ms | Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 005-ms | Method of Sections
Problem 005-ms
The structure shown in Figure T-07 is pinned to the floor at A and H. Determine the magnitude of all the
support forces acting on the structure and find the force in member BF.
Solution 005-ms
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints
1/5
2/2/2019
Problem 005-ms | Method of Sections | Engineering Mechanics Review
Click here to show or hide the solution
Member GH is axial hence; it can only transmit vertical force to the support at H.
ΣMA = 0
1.2RH = 1.2(100) + 4.5(80)
RH = 400 kN upward
answer
ΣMH = 0
1.2AV = 4.5(80)
AV = 300 kN downward
answer
ΣFH = 0
AH = 80 kN to the left
answer
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints
2/5
2/2/2019
Problem 005-ms | Method of Sections | Engineering Mechanics Review
If you wish to check the reaction forces at A and H, pass a cutting plane through members AB, AG, and
AH. As shown in the figure above, the cutting plane b-b cut these members. Take the section above b-b
and replace the cut members by internal force to maintain equilibrium. Solve for the internal force in
members AB, AG, and AH. With these forces known, you can then check the reactions through joints A
and H. The free body diagram of the section above b-b is similar to the free body diagram of section
above a-a. See the solution of section a-a below for easy reference of doing the section b-b.
From section above a-a
ΣFH = 0
4
√41
FBF = 80
answer
FBF = 128.06 kN tension
Tags:
Truss Truss member Truss Reaction
example of method of sections
Method of Sections
‹ Problem 004-ms | Method of Sections
Subscribe to MATHalino.com on
Custom Search
YouTube
up
Truss Analysis
Problem 417 - Roof Truss by Method of
Sections ›
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints
3/5
2/2/2019
Problem 005-ms | Method of Sections | Engineering Mechanics Review
Accounting
Scholarships
UNICAF Scholarships
UNICAF Scholarships for BSc in
Accounting and Finance with 9 ACCA
Exemptions
OPEN
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
Problem 418 - Warren Truss by Method of Sections
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints
4/5
2/2/2019
Problem 005-ms | Method of Sections | Engineering Mechanics Review
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-005-mj-method-joints
5/5
2/2/2019
Problem 403 | Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 403 | Method of Joints
Problem 403
Determine the force in each bar of the truss shown in Fig. P-403.
Solution 403
Click here to show or hide the solution
By symmetry
RA = RG = 0.5P
From joint D
ΣFH = 0
FC D cos 60
∘
= FDE cos 60
∘
FC D = FDE
ΣFV = 0
FC D sin 60
FDE sin 60
∘
∘
+ FDE sin 60
+ FDE sin 60
∘
∘
= P
= P
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints
1/6
2/2/2019
2FDE sin 60
Problem 403 | Method of Joints | Engineering Mechanics Review
∘
= P
FDE = 0.5774P
compression
Hence,
FC D = 0.5774P
compression
From joint C
FBC = FC D
FBC = 0.5774P
compression
FC E = 0
FC F = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints
2/6
2/2/2019
Problem 403 | Method of Joints | Engineering Mechanics Review
From joint E
FEF = FDE
FEF = 0.5774P
compression
From joint A
FAB = RA
FAB = 0.5P
compression
FAH = 0
From joint G
FF G = RG
FF G = 0.5P
compression
FGH = 0
From joint H
FF H = 0
FBH = 0
From joint B
ΣFH = 0
FBF = FBC cos 60
∘
FBF = 0.5774P cos 60
FBF = 0.2887P
∘
tension
Summary
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints
3/6
2/2/2019
Problem 403 | Method of Joints | Engineering Mechanics Review
Tags: Truss
Truss member
Truss Reaction
‹ Problem 005-mj | Method of Joints
Subscribe to MATHalino.com on
Custom Search
Method of Joints
up
YouTube
Zero Stress
Problem 404 Roof Truss - Method of Joints
›
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints
4/6
2/2/2019
Problem 403 | Method of Joints | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints
5/6
2/2/2019
Problem 403 | Method of Joints | Engineering Mechanics Review
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints
6/6
2/2/2019
Problem 404 Roof Truss - Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 404 Roof Truss - Method of Joints
Problem 404
Determine the forces in the members of the roof truss shown in Fig. P-404.
Solution 404
Click here to show or hide the solution
ΣMD = 0
2xRA = 450x
RA = 225 N
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints-0
1/5
2/2/2019
Problem 404 Roof Truss - Method of Joints | Engineering Mechanics Review
ΣMA = 0
∘
2xVD = 450x + (450 sin 30 )(2x)
VD = 450 N
ΣFH = 0
H D = 450 cos 30
∘
= 389.71 N
At Joint A
ΣFV = 0
FAB sin 30
∘
= 225
FAB = 450 N
ΣFH = 0
FAC = FAB cos 30
∘
= 450 cos 30
∘
FAC = 389.71 N
At Joint C
ΣFV = 0
FBC = 450 N
ΣFH = 0
FC D = 389.71 N
At Joint B
ΣFH = 0
FBD cos 30
∘
= 450 cos 30
∘
+ 450 cos 30
∘
FBD = 900 N
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints-0
2/5
2/2/2019
Problem 404 Roof Truss - Method of Joints | Engineering Mechanics Review
ΣFV = 0
FBD sin 30
∘
+ 450 sin 30
∘
= 450 + 450 sin 30
∘
Check!
FBD = 900 N
At Joint D
ΣFV = 0
450 = 900 sin 30
450 = 450
∘
Check!
ΣFH = 0
900 cos 30
∘
= 389.71 + 389.71
779.42 = 779.42
Check!
Summary
AB = 450 N compression
AC = 389.71 N tension
BC = 450 N tension
BD = 900 N compression
CD = 389.71 N tension
Tags: Truss
Truss member
roof truss
Method of Joints
‹ Problem 403 | Method of Joints
up
Problem 405 | Method of Joints ›
FEA for Dummies
The intro before the intro
We know FEA. Get the knowledge you
need from NAFEMS.
nafems.org
OPEN
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints-0
3/5
2/2/2019
Problem 404 Roof Truss - Method of Joints | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints-0
4/5
2/2/2019
Problem 404 Roof Truss - Method of Joints | Engineering Mechanics Review
Dynamics
Force Systems in Space
Like us on Facebook
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-403-method-joints-0
5/5
2/2/2019
Problem 405 | Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 405 | Method of Joints
Problem 405
Determine the force in each bar of the truss shown in Fig. P-405 caused by lifting the 120 kN load at a
constant velocity of 8 m per sec. What change in these forces, if any, results from placing the roller support
at D and the hinge support at A?
Solution 405
Click here to show or hide the solution
The load is lifted at constant velocity (in dynamic equilibrium),
thus, the forces involve is similar to forces under static
equilibrium.
ΣFV = 0
C V = 120 + 120(
3
5
)
C V = 192 kN
ΣFH = 0
C H = 120(
4
5
)
https://www.mathalino.com/reviewer/engineering-mechanics/problem-405-method-joints
1/5
2/2/2019
Problem 405 | Method of Joints | Engineering Mechanics Review
C H = 96 kN
By symmetry of vertical forces
RA = D V =
1
2
(192)
RA = D V = 96 kN
ΣFH = 0
D H = 96 kN
At Joint A
ΣFV = 0
FAB (
3
5
) = 96
FAB = 160 kN
ΣFH = 0
FAC =
4
5
FAB =
4
5
(160)
FAC = 128 kN
At Joint C
ΣFV = 0
FBC = 192 kN
ΣFH = 0
FC D + 96 = 128
FC D = 32 kN
https://www.mathalino.com/reviewer/engineering-mechanics/problem-405-method-joints
2/5
2/2/2019
Problem 405 | Method of Joints | Engineering Mechanics Review
At Joint B
ΣFH = 0
FBD (
4
5
) = 160(
4
5
)
FBD = 160 kN
ΣFV = 0
FBD (
160(
3
5
3
5
) + 160(
) + 160(
3
5
3
5
) = 192
) = 192
Check!
192 = 192
At Joint D
ΣFV = 0
96 = 160(
96 = 96
3
5
)
Check!
ΣFH = 0
32 + 96 = 160(
128 = 128
4
5
)
Check!
Summary
AB = 160 kN compression
AC = 128 kN tension
BC = 192 kN tension
CD = 32 kN tension
BD = 160 kN compression
With the roller support at D and the hinge support at A
Click here to show or hide the solution
Tags: dynamic equilibrium
Truss
‹ Problem 404 Roof Truss - Method of
Truss member
Method of Joints
up
Joints
https://www.mathalino.com/reviewer/engineering-mechanics/problem-405-method-joints
Problem 406 Cantilever Truss - Method of
Joints ›
3/5
2/2/2019
Problem 405 | Method of Joints | Engineering Mechanics Review
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
Try it free for 14 days
Create, edit, store and share les in your browser
and across devices.
OPEN
G Suite by Google Cloud
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
https://www.mathalino.com/reviewer/engineering-mechanics/problem-405-method-joints
4/5
2/2/2019
Problem 405 | Method of Joints | Engineering Mechanics Review
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-405-method-joints
5/5
2/2/2019
Problem 406 Cantilever Truss - Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 406 Cantilever Truss - Method of Joints
Problem 406
The cantilever truss in Fig. P-406 is hinged at D and E. Find the force in each member.
Solution 406
Click here to show or hide the solution
At Joint A
ΣFV = 0
FAB sin 30
∘
= 1000
FAB = 2000 N
tension
ΣFH = 0
FAC = FAB cos 30
∘
FAC = 2000 cos 30
FAC = 1732.05 N
∘
compression
https://www.mathalino.com/reviewer/engineering-mechanics/problem-406-cantilever-truss-method-joints
1/4
2/2/2019
Problem 406 Cantilever Truss - Method of Joints | Engineering Mechanics Review
At Joint B
ΣFy = 0
FBC = 1000 cos 30
FBC = 866.02 N
∘
compression
ΣFx = 0
FBD = 1000 sin 30
FBD = 2500 N
∘
+ 2000
tension
At Joint C
ΣFV = 0
FC D sin 60
∘
= 866.02 sin 60
∘
+ 1000
tension
FC D = 2020.72 N
ΣFH = 0
FC E = FC D cos 60
∘
+ 866.02 cos 60
FC E = 2020.72 cos 60
FC E = 3175.42 N
∘
∘
+ 1732.05
+ 866.02 cos 60
∘
+ 1732.05
compression
Summary
AB = 2000 N tension
AC = 1732.05 N compression
BC = 866.02 N compression
BD = 2500 N tension
CD = 2020.72 N tension
CE = 3175.42 N compression
Tags: cantilever truss
Method of Joints
‹ Problem 405 | Method of Joints
Truss
Truss member
up
rotated axes
Problem 407 Cantilever Truss - Method of
Joints ›
https://www.mathalino.com/reviewer/engineering-mechanics/problem-406-cantilever-truss-method-joints
2/4
2/2/2019
Problem 406 Cantilever Truss - Method of Joints | Engineering Mechanics Review
-60%
-49%
₦ 6,250
-63%
₦ 1,800
₦ 69,480
₦ 108,500
₦ 92,500
-37%
₦ 93,000
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
What does your name mean
Diagnose you by your name. You can also create
your diagnosis.
OPEN
shindanmaker.com
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
https://www.mathalino.com/reviewer/engineering-mechanics/problem-406-cantilever-truss-method-joints
3/4
2/2/2019
Problem 406 Cantilever Truss - Method of Joints | Engineering Mechanics Review
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-406-cantilever-truss-method-joints
4/4
2/2/2019
Problem 407 Cantilever Truss - Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 407 Cantilever Truss - Method of Joints
Problem 407
In the cantilever truss shown in Fig. P-407, compute the force in members AB, BE, and DE.
Solution 407
Click here to show or hide the solution
At Joint A
ΣFy = 0
FAC sin 30
∘
= 1000
FAC = 2000 lb
compression
ΣFx = 0
FAB = FAC cos 30
∘
FAB = 2000 cos 30
FAB = 1732.05 lb
∘
tension
At Joint C
ΣFV = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-cantilever-truss-method-joints
1/5
2/2/2019
Problem 407 Cantilever Truss - Method of Joints | Engineering Mechanics Review
FBC = 0
ΣFH = 0
FC E = 2000 lb
compression
At Joint B
ΣFy = 0
FBE sin 60
∘
= 1000
FBE = 1154.70 lb
compression
From the FBD of the whole truss shown below
b = 3a sin 30
∘
b = 1.5a
Solve for the reaction at support H
ΣMG = 0
RH (b) = 1000(3a) + 1000(2a) + 1000(a)
RH (1.5a) = 6000a
RH = 4000 lb
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-cantilever-truss-method-joints
2/5
2/2/2019
Problem 407 Cantilever Truss - Method of Joints | Engineering Mechanics Review
Thus,
FEH = 4000 lb
compression
At Joint E
ΣFH = 0
FEF cos 60
∘
+ 1154.70 sin 60
FEF = 2000 lb
∘
+ 2000 = 4000
tension
ΣFV = 0
FDE + 1154.70 cos 60
FDE + 1154.70 cos 60
FDE = 1154.7 lb
∘
∘
= FEF sin 60
∘
= 2000 sin 60
∘
compression
We may check FDE by Method of Sections (Optional)
ΣMG = 0
∘
FDE (a cos 30 ) = 1000a
FDE = 1154.7 lb
compression
Check!
Summary (Answers)
AB = 1732.05 lb tension
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-cantilever-truss-method-joints
3/5
2/2/2019
Problem 407 Cantilever Truss - Method of Joints | Engineering Mechanics Review
BE = 1154.70 lb compression
DE = 1154.70 lb compression
Tags:
Method of Joints
rotated axes
Method of Sections
cantilever truss
‹ Problem 406 Cantilever Truss - Method of
Joints
up
Truss
Truss member
Truss Analysis
Problem 408 Warren Truss - Method of
Joints ›
-35%
₦ 4,000
₦ 93,000
Nationwide Delivery
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
MATHalino
YouTube
3K
Engineering Mechanics
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-cantilever-truss-method-joints
4/5
2/2/2019
Problem 407 Cantilever Truss - Method of Joints | Engineering Mechanics Review
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-cantilever-truss-method-joints
5/5
2/2/2019
Problem 408 Warren Truss - Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 408 Warren Truss - Method of Joints
Problem 408
Compute the force in each member of the Warren truss shown in Fig. P-408.
Solution 408
Click here to show or hide the solution
ΣME = 0
20RA = 1000(15) + 4000(10) + 3000(5)
RA = 3500 lb
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-warren-truss-method-joints
1/5
2/2/2019
Problem 408 Warren Truss - Method of Joints | Engineering Mechanics Review
ME = 0
20RE = 1000(5) + 4000(10) + 3000(15)
RE = 4500 lb
At Joint A
ΣFV = 0
FAB sin 60
∘
= 3500
compression
FAB = 4041.45 lb
ΣFH = 0
FAC = FAB cos 60
∘
FAC = 4041.45 cos 60
FAC = 2020.72 lb
∘
tension
At Joint B
ΣFV = 0
FBC sin 60
∘
+ 1000 = 4041.45 sin 60
FBC = 2886.75 lb
∘
tension
ΣFH = 0
FBD = 4041.45 cos 60
FBD = 4041.45 cos 60
FBD = 3464.10 lb
∘
∘
+ FBC cos 60
∘
+ 2886.75 cos 60
∘
compression
At Joint C
ΣFV = 0
FC D sin 60
∘
+ 2886.75 sin 60
FC D = 1732.05 lb
∘
= 4000
tension
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-warren-truss-method-joints
2/5
2/2/2019
Problem 408 Warren Truss - Method of Joints | Engineering Mechanics Review
ΣFH = 0
FC E + FC D cos 60
∘
= 2020.72 + 2886.75 cos 60
FC E + 1732.05 cos 60
FC E = 2598.07 lb
∘
∘
= 2020.72 + 2886.75 cos 60
∘
tension
At Joint D
ΣFV = 0
FDE sin 60
∘
= 1732.05 sin 60
FDE = 5196.15 lb
∘
+ 3000
compression
ΣFH = 0
FDE cos 60
∘
+ 1732.05 cos 60
5196.15 cos 60
∘
∘
= 3464.10
+ 1732.05 cos 60
3464.10 = 3464.10
∘
= 3464.10
Check!
At Joint E
ΣFV = 0
5196.15 sin 60
∘
= 4500
Check!
4500 = 4500
ΣFH = 0
5196.15 cos 60
∘
= 2598.07
2598.07 = 2598.07
Check!
Summary
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-warren-truss-method-joints
3/5
2/2/2019
Problem 408 Warren Truss - Method of Joints | Engineering Mechanics Review
AB = 4041.45 lb compression
AC = 2020.72 lb tension
BC = 2886.75 lb tension
BD = 3464.10 lb compression
CD = 1732.05 lb tension
CE = 2598.07 lb tension
DE = 5196.15 lb compression
Tags: Warren Truss
Method of Joints
Truss
‹ Problem 407 Cantilever Truss - Method of
Truss Analysis
up
Problem 409 Howe Roof Truss - Method of
Joints
Joints ›
Temporary Bridges
We supply effective emergency,
temporary and permanent bridges
OPEN
retrobridge.com
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
S8 3D HiFi
Wireless
₦ 10,000
Bluetooth Mini
Speaker With…
S812 Bluetooth
₦ 5,000
Speaker
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-warren-truss-method-joints
4/5
2/2/2019
Problem 408 Warren Truss - Method of Joints | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-407-warren-truss-method-joints
5/5
2/2/2019
Problem 409 Howe Roof Truss - Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 409 Howe Roof Truss - Method of Joints
Problem 409
Determine the force in members AB, BD, BE, and DE of the Howe roof truss shown in Fig. P-409.
Solution 409
Click here to show or hide the solution
ΣMH = 0
12RA = 9(2.7) + 6(4.5) + 3(1.8)
RA = 4.725 kN
https://www.mathalino.com/reviewer/engineering-mechanics/problem-409-howe-roof-truss-method-joints
1/4
2/2/2019
Problem 409 Howe Roof Truss - Method of Joints | Engineering Mechanics Review
At Joint A
ΣFV = 0
FAB sin 30
∘
= 4.725
compression
FAB = 9.45 kN
answer
At Joint C
By inspection
FBC = 2.7 kN
tension
At Joint B
By inspection
FBE = 2.7 kN
compression
answer
ΣFx = 0
FBD + FBE cos 60
FBD + 2.7 cos 60
FBD = 6.75 kN
∘
∘
+ 2.7 cos 60
+ 2.7 cos 60
∘
∘
= 9.45
= 9.45
compression
answer
At Joint D
By inspection
FDF = 6.75 kN
compression
ΣFV = 0
FDE = FDF sin 30
FDE = 6.75 sin 30
FDE = 6.75 kN
Tags: Howe truss
∘
∘
+ 6.75 sin 30
+ 6.75 sin 30
tension
∘
∘
answer
roof truss
Truss
‹ Problem 408 Warren Truss - Method of
Joints
Truss Analysis
up
Method of Joints
Problem 410 Pratt Roof Truss - Method of
Joints ›
https://www.mathalino.com/reviewer/engineering-mechanics/problem-409-howe-roof-truss-method-joints
2/4
2/2/2019
Problem 409 Howe Roof Truss - Method of Joints | Engineering Mechanics Review
-37%
₦ 7,900
₦ 93,000
Get 5% off with Jumia Pay
Subscribe to MATHalino.com on
YouTube
3K
Search
₦ 5,990
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
https://www.mathalino.com/reviewer/engineering-mechanics/problem-409-howe-roof-truss-method-joints
3/4
2/2/2019
Problem 409 Howe Roof Truss - Method of Joints | Engineering Mechanics Review
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-409-howe-roof-truss-method-joints
4/4
2/2/2019
Problem 410 Pratt Roof Truss - Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 410 Pratt Roof Truss - Method of Joints
Problem 410
Determine the force in each member of the Pratt roof truss shown in Fig. P-410.
Solution 410
Click here to show or hide the solution
By symmetry
RA = RH =
1
2
(3 × 8)
RA = RH = 12 kN
https://www.mathalino.com/reviewer/engineering-mechanics/problem-410-pratt-roof-truss-method-joints
1/5
2/2/2019
Problem 410 Pratt Roof Truss - Method of Joints | Engineering Mechanics Review
At Joint A
ΣFV = 0
FAB sin α = 12
FAB (
3
5
) = 12
compression
FAB = 20 kN
ΣFH = 0
FAC = FAB cos α
FAC = 20(
4
5
)
tension
FAC = 16 kN
At Joint B
By inspection
compression
FBD = 20 kN
FBC = 8 kN
compression
At Joint C
ΣFV = 0
FC D sin β = 8
FC D (
3
) = 8
√13
FC D = 9.6148 kN
tension
ΣFH = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-410-pratt-roof-truss-method-joints
2/5
2/2/2019
Problem 410 Pratt Roof Truss - Method of Joints | Engineering Mechanics Review
FC E + FC D cos β = 16
FC E + 9.6148(
2
√13
) = 16
FC E = 10.6667 kN
tension
At Joint E
By inspection
FDE = 0
Summary
AB = FH = 20 kN compression
AC = GH = 16 kN tension
BC = FG = 8 kN compression
BD = DF = 20 kN compression
CD = DG = 9.6148 kN tension
CE = EG = 10.6667 kN tension
DE = 0
Tags:
Pratt truss roof truss
symmetrical forces
Method of Joints
‹ Problem 409 Howe Roof Truss - Method
of Joints
Truss
up
Truss Analysis
Truss member
symmetrical load
Problem 411 Cantilever Truss by Method of
Joints ›
https://www.mathalino.com/reviewer/engineering-mechanics/problem-410-pratt-roof-truss-method-joints
3/5
2/2/2019
Problem 410 Pratt Roof Truss - Method of Joints | Engineering Mechanics Review
-60%
-35%
-63%
-37%
Cash on Delivery
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
₦ 109,000
₦ 143,000
₦ 1,828
₦ 10,000
₦ 95,000
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
https://www.mathalino.com/reviewer/engineering-mechanics/problem-410-pratt-roof-truss-method-joints
4/5
2/2/2019
Problem 410 Pratt Roof Truss - Method of Joints | Engineering Mechanics Review
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-410-pratt-roof-truss-method-joints
5/5
2/2/2019
Problem 413 Crane by Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 413 Crane by Method of Joints
Problem 413
Determine the force in each member of the crane shown in Fig. P-413.
Solution 413
Click here to show or hide the solution
tan θ =
2
4
∘
θ = 26.56
30
30
∘
∘
∘
+ θ = 30 + 26.56
∘
+ θ = 56.56
https://www.mathalino.com/reviewer/engineering-mechanics/problem-413-crane-method-joints
1/4
2/2/2019
Problem 413 Crane by Method of Joints | Engineering Mechanics Review
Apply Cosine law to triangle ABC
b
2
= 2
2
+ 3
2
− 2(2 × 3) cos(30
∘
∘
+ 90 )
−
−
b = √19 m = 4.36 m
b
sin(30
∘
sin α =
2
=
∘
sin α
+ 90 )
2 sin 120
∘
−
−
√19
∘
α = 23.41
At Joint A
ΣFV = 0
FAC sin α = 52
∘
FAC sin 23.41
= 52
tension
FAC = 131 kN
ΣFH = 0
FAB = FAC cos α
∘
FAB = 131 cos 23.41
compression
FAB = 120 kN
At Joint B
ΣFy = 0
FBC = 120 sin 30
∘
compression
FBC = 60 kN
ΣFx = 0
FBD = 120 cos 30
∘
compression
FBD = 104 kN
At Joint C
ΣFV = 0
FC D sin(30
∘
+ θ) + 60 cos 30
∘
FC D sin 56.56
+ 60 cos 30
∘
∘
= 131 sin α
∘
= 131 sin 23.41
FC D = 0
ΣFH = 0
FC E + 60 sin 30
FC E + 60 sin 30
FC E = 90 kN
∘
∘
= 131 cos α
∘
= 131 cos 23.41
tension
https://www.mathalino.com/reviewer/engineering-mechanics/problem-413-crane-method-joints
2/4
2/2/2019
Problem 413 Crane by Method of Joints | Engineering Mechanics Review
Summary
AC = 131 kN tension
AB = 120 kN compression
BC = 60 kN compression
BD = 104 kN compression
CD = 0
CE = 90 kN tension
Tags: Method of Joints
crane
rotated axes
‹ Problem 412 Right Triangular Truss by
Method of Joints
up
Problem 414 Truss by Method of Joints ›
Top Hoist
Manufacturer China
100% Factroy Price, ISO & CE
All Types of Hoists From 0.5-32ton.
More Discount Here. Visit Now!
OPEN
ytcrane.com
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
Get the USA Products You Want
Sign Up Today for a MyUS Address.
Fast & Reliable Shipping to Your
Home
MATHalino
YouTube
3K
https://www.mathalino.com/reviewer/engineering-mechanics/problem-413-crane-method-joints
3/4
2/2/2019
Problem 413 Crane by Method of Joints | Engineering Mechanics Review
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-413-crane-method-joints
4/4
2/2/2019
Problem 414 Truss by Method of Joints | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 414 Truss by Method of Joints
Problem 414
Determine the force in members AB, BD, and CD of the truss shown in Fig. P-414. Also solve for the force on
members FH, DF, and DG.
Solution 414
Click here to show or hide the solution
Solving for force in members AB, BD, and CD
ΣMH = 0
12RA = 9(30) + 6(30) + 3(90)
RA = 60 kN
https://www.mathalino.com/reviewer/engineering-mechanics/problem-414-truss-method-joints
1/5
2/2/2019
Problem 414 Truss by Method of Joints | Engineering Mechanics Review
At Joint A
ΣFV = 0
1
√2
FAB = 60
compression
FAB = 84.85 kN
answer
At Joint B
ΣFH = 0
3
√10
FBD =
1
√2
(84.85)
compression
FBD = 63.24 kN
answer
ΣFV = 0
FBC +
FBC +
1
√10
1
FBD =
1
(84.85)
√2
(63.24) =
√10
FBC = 40 kN
1
(84.85)
√2
tension
At Joint C
ΣFV = 0
4
5
FC D + 30 = 40
FC D = 12.5 kN
compression
answer
Summary
AB = 84.85 kN compression
BD = 63.24 kN compression
CD = 12.5 kN compression
https://www.mathalino.com/reviewer/engineering-mechanics/problem-414-truss-method-joints
2/5
2/2/2019
Problem 414 Truss by Method of Joints | Engineering Mechanics Review
Solving for force in members FH, DF, and DG
ΣMA = 0
12RH = 3(30) + 6(30) + 9(90)
RH = 90 kN
At Joint H
ΣFV = 0
1
√2
FF H = 90
FF H = 127.28 kN
compression
answer
At Joint F
ΣFH = 0
3
√10
FDF =
1
√2
(127.28)
compression
FDF = 94.87 kN
answer
ΣFH = 0
FF G +
FF G +
1
√10
1
FDF =
1
(127.28)
√2
(94.87) =
√10
FF G = 60 kN
1
(127.28)
√2
tension
At Joint G
ΣFV = 0
4
5
FDG + 60 = 90
FDG = 37.5 kN
tension
answer
https://www.mathalino.com/reviewer/engineering-mechanics/problem-414-truss-method-joints
3/5
2/2/2019
Problem 414 Truss by Method of Joints | Engineering Mechanics Review
Summary
FH = 127.28 kN compression
DF = 94.87 kN compression
DG = 37.5 kN tension
Tags: Truss
Method of Joints
Truss Analysis
‹ Problem 413 Crane by Method of Joints
up
Method of Sections | Analysis of Simple
Trusses ›
Get the USA
Products You Want
Sign Up Today for a MyUS Address. Fast
& Reliable Shipping to Your Home
MyUs.com
OPEN
Subscribe to MATHalino.com on
Custom Search
YouTube
3K
Search
Ready for your
next promotion.
A Mancosa MBA
makes it
possible.
For US $350 per
month.
ENROL NOW >>
https://www.mathalino.com/reviewer/engineering-mechanics/problem-414-truss-method-joints
4/5
2/2/2019
Problem 414 Truss by Method of Joints | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Problem 001-mj | Method of Joints
Problem 002-mj | Method of Joints
Problem 003-mj | Method of Joints
Problem 004-mj | Method of Joints
Problem 005-mj | Method of Joints
Problem 403 | Method of Joints
Problem 404 Roof Truss - Method of Joints
Problem 405 | Method of Joints
Problem 406 Cantilever Truss - Method of Joints
Problem 407 Cantilever Truss - Method of Joints
Problem 408 Warren Truss - Method of Joints
Problem 409 Howe Roof Truss - Method of Joints
Problem 410 Pratt Roof Truss - Method of Joints
Problem 411 Cantilever Truss by Method of Joints
Problem 412 Right Triangular Truss by Method of Joints
Problem 413 Crane by Method of Joints
Problem 414 Truss by Method of Joints
Method of Sections | Analysis of Simple Trusses
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-414-truss-method-joints
5/5
2/2/2019
Problem 417 - Roof Truss by Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 417 - Roof Truss by Method of Sections
Problem 417
Using the method of sections, determine the force in members BD, CD, and CE of the roof truss shown in
Fig. P-417.
Solution 417
Click here to show or hide the solution
ΣMF = 0
12RA = 4(360)
RA = 120 kN
ΣMC = 0
3FBD = 4(120)
FBD = 160 kN
compression
answer
https://www.mathalino.com/reviewer/engineering-mechanics/problem-417-roof-truss-method-sections
1/4
2/2/2019
Problem 417 - Roof Truss by Method of Sections | Engineering Mechanics Review
ΣFV = 0
3
5
FC D = 120
FC D = 200 kN
compression
answer
ΣMD = 0
3FC E = 8(120)
FC E = 320 kN
Tags: roof truss
tension
answer
Method of Sections
Truss
‹ Problem 005-ms | Method of Sections
Subscribe to MATHalino.com on
Custom Search
YouTube
Truss member
up
Problem 418 - Warren Truss by Method of
Sections ›
3K
Search
https://www.mathalino.com/reviewer/engineering-mechanics/problem-417-roof-truss-method-sections
2/4
2/2/2019
Problem 417 - Roof Truss by Method of Sections | Engineering Mechanics Review
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
Problem 418 - Warren Truss by Method of Sections
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-417-roof-truss-method-sections
3/4
2/2/2019
Problem 417 - Roof Truss by Method of Sections | Engineering Mechanics Review
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
Like us on Facebook
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-417-roof-truss-method-sections
4/4
2/2/2019
Problem 418 - Warren Truss by Method of Sections | Engineering Mechanics Review
MATHalino
Engineering Mathematics
Home
Algebra
Trigonometry
Geometry
Calculus
Mechanics
CE Math
Problem 418 - Warren Truss by Method of Sections
Problem 418
The Warren truss loaded as shown in Fig. P-418 is supported by a roller at C and a hinge at G. By the method
of sections, compute the force in the members BC, DF, and CE.
Solution 418
Click here to show or hide the solution
https://www.mathalino.com/reviewer/engineering-mechanics/problem-418-warren-truss-method-sections
1/4
2/2/2019
Problem 418 - Warren Truss by Method of Sections | Engineering Mechanics Review
ΣMG = 0
12RC + 6(60) = 6(100) + 9(80) + 18(40)
RC = 140 kN
At section through M-M
ΣFV = 0
2
√5
FBC = 40
FBC = 44.721 kN
compression
answer
At section through N-N
ΣMD = 0
6FC E + 9(40) = 3(140)
FC E = 10 kN
tension
answer
ΣME = 0
https://www.mathalino.com/reviewer/engineering-mechanics/problem-418-warren-truss-method-sections
2/4
2/2/2019
Problem 418 - Warren Truss by Method of Sections | Engineering Mechanics Review
6FDF + 3(80) + 12(40) = 6(140) + 6(60)
FDF = 80 kN
compression
Tags: Warren Truss
answer
Method of Sections
Truss member
‹ Problem 417 - Roof Truss by Method of
Sections
Subscribe to MATHalino.com on
Custom Search
YouTube
up
overhanging truss
Truss
Problem 419 - Warren Truss by Method of
Sections ›
3K
Search
MATHalino
YouTube
3K
Engineering Mechanics
Principles of Statics
Equilibrium of Force System
Analysis of Structures
Method of Joints | Analysis of Simple Trusses
Method of Sections | Analysis of Simple Trusses
Problem 001-ms | Method of Sections
Problem 002-ms | Method of Sections
Problem 003-ms | Method of Sections
Problem 004-ms | Method of Sections
Problem 005-ms | Method of Sections
Problem 417 - Roof Truss by Method of Sections
Problem 418 - Warren Truss by Method of Sections
https://www.mathalino.com/reviewer/engineering-mechanics/problem-418-warren-truss-method-sections
3/4
2/2/2019
Problem 418 - Warren Truss by Method of Sections | Engineering Mechanics Review
Problem 419 - Warren Truss by Method of Sections
Problem 420 - Howe Truss by Method of Sections
Problem 421 - Cantilever Truss by Method of Sections
Problem 422 - Right-triangular Truss by Method of Sections
Problem 423 - Howe Roof Truss by Method of Sections
Problem 424 - Method of Joints Checked by Method of Sections
Problem 425 - Fink Truss by Method of Sections
Problem 426 - Fink Truss by Method of Sections
Problem 427 - Interior Members of Nacelle Truss by Method of Sections
Problem 428 - Howe Truss by Method of Sections
Problem 429 - Cantilever Truss by Method of Sections
Problem 430 - Parker Truss by Method of Sections
Problem 431 - Members in the Third Panel of a Parker Truss
Problem 432 - Force in Members of a Truss by Method of Sections
Problem 433 - Scissors Truss by Method of Sections
Problem 434 - Scissors Truss by Method of Sections
Problem 435 - Transmission Tower by Method of Sections
Problem 436 - Howe Truss With Counter Braces
Problem 437 - Truss With Counter Diagonals
Problem 438 - Truss With Redundant Members
Method of Members | Frames Containing Three-Force Members
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
MATHalino
Like Page
39K likes
Home • Forums • Blogs • Glossary • Recent
About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal
MATHalino.com - Pinoy Math Community • Copyright 2018 © Romel Verterra • All rights reserved
View Stat Details
https://www.mathalino.com/reviewer/engineering-mechanics/problem-418-warren-truss-method-sections
4/4