MEMB 123 Semester 1 2013-2014
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03/12/2013 MEMB 123 Semester 1 2013-2014
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MEMB 123
Semester 1
2013-2014
Project 1
Lecturer: Dr.Abreeza Noorlina Bte Abd.Manap
Student Name: Omer Hamza Babiker
ID: EP091010
SECTION: 03A
8 Pages
Sub Date
Project Description
A bridge having a horizontal top cord is to span between the two piers A and Bhaving an arbitrary height. It is required that a pin-connected truss be used,consisting of steel members bolted together to steel gusset plates, such as the oneshown in Figure 1. The end supports are assumed to be a pin at A and a roller at B.A vertical loading of 5 kN is to be supported within the middle 3 m of the span.
03/12/2013 MEMB 123 Semester 1 2013-2014
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This load can be applied in part to several joints on the top cord within this region,or to a single joint at the middle of the top cord. The weights of the members are tobe neglected. Assume the maximum tensile force in each member cannot exceed4.25 kN; and regardless of the length of the member, the maximum compressiveforce cannot exceed 3.5 kN.
Design the most economical truss that will support the loading. The memberscost $7.50/m, and the gusset plates cost $8.00 each. Submit a report on the costanalysis as well as a complete force analysis along with the scaled drawing of thetruss, identifying on this drawing the tensile and compressive force in each member.
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Info:
A hoist support designed specifically to hold at least 5000 Newton or 500 kilogram of loads A bridge
having a horizontal top cord is to span between the two piers A and B having an arbitrary height. It is
required that a pin-connected truss be used, consisting of steel members bolted together to steel gusset
plates. The end supports are assumed to be a pin at A and a roller at B. A vertical loading of 5 kN is to
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03/12/2013 MEMB 123 Semester 1 2013-2014
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be supported within the middle 3 m of the span. This load can be applied in part to several joints on the
top cord within this region, or to a single joint at the middle of the top cord. The weights of the members
are to be neglected. Assume the maximum tensile force in each member cannot exceed 4.25 kN; and
regardless of the length of the member, the maximum compressive force cannot exceed 3.5 kN. With
minimal usage of materials, and cost .
Goals:
1- the bridge must be able to lift a load of a specified weight and the second is
that the bridge must remain stable and not topple over when the load is lifted
and moved to another location.
2- see practical applications for trigonometry, physics, and statics.
3- must the hoist support is extremely stable and can hold the given load.
4- measuring and all the data had been recorded as we may refer to it whenever
we need to calculate and build our prototype.
5- cultivate leadership within the team. As a team, we need a leader to ensure the
effectiveness of each member.
Tools :
Trusses are composed of slender bars that are assumed to carry only
6- The leader plays a big role and this will grant the task to complete due to
datelines given.
03/12/2013 MEMB 123 Semester 1 2013-2014
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axial force. Joints in large trusses are formed by welding or boltingmembers to gusset plates. (see fig a ).
The members of most modern trusses are arranged in triangular patterns becauseeven when the joints are pinned, the triangular form is geometrically stable and willnot collapse under load (see fig b ).
Similarly, we can imagine that joint E is formed by
extending bars from joints C and D. Trusses formed in this manner arecalled simple trusses. (see fig c ).
A truss is completely analyzed when the magnitude and sense (tension orcompression) of all bar forces and reactions are determined.
Because all forces acting at a joint pass through the pin, they constitute aconcurrent force system. For this type of force system, only two
equations of statics (that is, _Fx = 0 and _Fy= 0) are available to evaluateunknown bar forces. Since only two equations of equilibrium are available, wecan only analyze joints that contain a maximum of two unknown bar forces.
(a)
(b)
(c)
Design:
03/12/2013 MEMB 123 Semester 1 2013-2014
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Calculation:
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03/12/2013 MEMB 123 Semester 1 2013-2014
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Conclusion:
Based on what we learnt in MEMB 123 subject I had applied the calculation to
03/12/2013 MEMB 123 Semester 1 2013-2014
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know receives extra force by the load to know when it may be broken by the time
and the hoist part that has to be strong enough to support the loads, Alsoensured the joining to be attached strongly and joining played their role bysupporting the force due to the load .Last I had learned that i can improve thestability by widen the base part by applied the calculation.
References :
1-www. Wikipedia.com2-Design of Building Trusses - James Ambrose3-Engineering Mechanics-STATICS- R. C. Hibbeler
To find support reeactios at A B.
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???=0
-2.5*4.5 -2.5(7.5)+By*12=0By=2.5 KN
???=0
Ax=0KN
???=0
-2.5 -2.5 =Ay+ 2.5=0Ay=2.5KN
Let ฮธ = 60ยฐTan(60)=(h/1.5)h=2.6 m
??=0atjont A
?
2.5 โ F * sin(60)=0F =2 . 89 KN
?
A
D
2.5KNC
2
ac ?ac
? = 0
-F + F *cos(60) =0
AF =1.44 KN
joint C
โ1 2.6
? 1
=50ยฐ
2.25
=tan
? ??=0
-2.89 * Cos(60) โF * Cos (50) +F = 0
โ??=0
2.89 * Sin(60) - F * Sin(50) = 0
F = 3.27 KN
F = 3.54 KN
Joint D A
? ??=0
1.44 โ Fde + 3.27 * Cos(50) + Fdf * Cos(50)=0
3.27 *Sin(50) โ 2.5 - F * Sin(50) = 0
F = 0 KN ( zero force member )
F = 3.5 KN
Joint E
???=0
D
ฮธF
C
2.5KN
DE
C
ฮธ ฮธ1
EG
D
F
ad ac
ad
ฮธ 1
( )
cd cf
cd
cd
cf
? ?? = 0
df
df
de
ef
1
1 F
03/12/2013 MEMB 123 Semester 1 2013-2014
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F = 0 KN ( zero force member )
???=0
-3.5 +F = 0
ef
ge
โ??=0
CF
F = 0 KN ( zero force member )
???=0
-F + F = 0F = F =3.54 KN
Joint G
G
H
F =3.5 KN
Joint FBy deleting previous zero force members at joints D , E . the forces at joint F looks like
By deleting previous zero force members at joints F . the forces at joint G looks like
2.5KN
G
???=0
E
B
-2.5 +F * Sin (50) =0
F =3.26 KN
ฮธ
???=0
H
3.5 โF โ 3.26 * Cos (50) = 0
F = 1.4 KN
Joint B
B
G
1.4 โ F * Cos(60) = 0
โ??=0
F = 2.8 KN
H
2.5KN
ฮธ
ge
fg
cf fh
fh cf
gh
gh 1
gb
gb
bh
bh
2
Joint H
To confirm the solution . we need to do force analysis at last joint HB
ฮธ1 ฮธ2
F H
03/12/2013 MEMB 123 Semester 1 2013-2014
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? ??=3.45+3.26โcos(50)+2.8โcos(60)=0
? ??=3.26โsin(50)+2.8โsin(60)=0
Member AC AD CD CF DE EG FH GH BH GBForce (KN) 2.89 1.44 3.26 3.54 3.5 3.5 3.54 3.26 2.8 1.4Force type T C C T C C T C T CT: tension force
C: compression force
The members DF, EF, and FG are zero force members .
the design met the specification where the maximum tensile force in each member cannot exceed 4.25kN; and regardless of the length of the member, the maximum compressive force cannot exceed 3.5kN.
1. COAST ANALYSIS
The members cost $7.50/m, and the gusset plates cost $8.00 each. We need to find the totallength of design members and number of gussets used .
Member AC AD CD CF DE EG FH GH BH GBLength (m) 3 4.5 3.5 4.5 1.5 1.5 4.5 3.5 3 4.5
The total length is (3+4.5+3.5+4.5+1.5+1.5+4.5+3.5+3+4.5=34 m)
Number of gussets =number of joints = 8
Total cost = 34*7.5 + 8*8 =319 $.