The bar in the figure has constant cross sectional area A. The top third of the bar, of length L, is made of a material with mass density ρ and Young's modulus E. The bottom two thirds of the bar (length 2L) is made of a different material, with density ρ/2 and Young's modulus 2E. The bar is fixed at the floor, C, at x=3L, and at the ceiling, B, at x=0. The bar deforms under its own weight. For a material with density ρ, gravity results in a load per unit volume ρg. No other loads are applied.
A , L , E , ρ , and g are KNOWN quantities.
Note that you must consider the gravity load on both segments of the bar as densities are different but comparable.
Q1_1_1 : 40.0 POINTS
Find a symbolic expression for the distributed load per unit length due to gravity fx(x), in terms of ρ, g, A (with ρ as rho):
for 0≤x<L, fx(x)=
unanswered
for L<x≤3L, fx(x)=
unanswered
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Q1_1_2 : 100.0 POINTS
Use the force method for statically indeterminate structures to obtain a symbolic expression for the reaction RCx at the support C in terms of ρ, g, A, L (with ρ written as rho):
RCx=
unanswered
You have used 0 of 3 submissions
Q1_1_3 : 40.0 POINTS
Obtain a symbolic expression for the axial force in the bar N(x) in terms of ρ, g, A, L, x (with ρwritten as rho):
for 0≤x<L, N(x)=
unanswered
for L<x≤3L, N(x)=
unanswered
You have used 0 of 3 submissions
Q1_1_4 : 80.0 POINTS
Obtain symbolic expressions for the maximum tensile and compressive stresses ( σmax,Tn and σmax,Cn )and their locations (coordinates xmax,T and xmax,C ) in terms of ρ, g, L (with ρ written asrho). (Note: enter the expressions for the stresses with their appropriate signs.)
σmax,Tn=
unanswered
at location xmax,T=
unanswered
σmax,Cn=
unanswered
at location xmax,C=
unanswered
You have used 0 of 3 submissions
Q1_1_5 : 60.0 POINTS
Obtain a symbolic expression for the displacement ux(x=2L) in terms of ρ, g, E, L (with ρwritten as rho):
ux(x=2L)=
unanswered
You have used 0 of 3 submissions
Q1_2 (QUIZ 1 PROBLEM 2): STATICALLY INDETERMINATE TRUSS PROBLEM WITH THE METHOD OF JOINTS
The truss in the figure is composed by 4 bars (AD, AC, BC, CD) connected by pins at A,B,C,D. The geometry of the truss is defined in the figure in terms of the length H of bar BC. A vertical load W=400kN is applied at joint D. A horizontal load 2W=800 kN is applied at joint C. The material of bar AC has modulus E0 and cross sectional area A0.
Q1_2_1 : 100.0 POINTS
(a) Use the method of joints to obtain the numerical values (in kN) of the axial forces in the four bars.
Note: there will be factors of 2√ in your solutions. Do not use the square root symbol in your answer, just factor in the value as 1.4142
NAD=
kN
unanswered
NAC=
kN
unanswered
NBC=
kN
unanswered
NCD=
kN
unanswered
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Q1_2_2 : 100.0 POINTS
(b) Obtain the value of the Cartesian components of reactions at the supports in kN.
RAx=
kN
unanswered
RAy=
kN
unanswered
RBx=
kN
unanswered
RBy=
kN
unanswered
You have used 0 of 3 submissions
Q1_2_3 : 40.0 POINTS
Obtain a symbolic expression for the elongation of the bar AC, δAC, in terms of H, W, E0, A0 (with E0 as E_0 and A0 as A_0):
δAC=
unanswered
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Q1_2_4 : 80.0 POINTS
Now assume that the bar BC is a composite bar obtained by bonding two cables: a steel cable with cross sectional area AS=1000 mm2, and an aluminum cable with cross sectional area AA, as shown in the figure, so that the total cross sectional area of the bar BC is AS+AA. Take the Young's modulus of steel to be ES=200 GPa, and the Young's modulus of aluminum to be EA=80 GPa.
If the failure stress of aluminum σA,fail=500 MPa, and we want a safety factor SF = 2 against failure, obtain the value (in mm2), of the minimum cross sectional area AA,min of aluminum that you should have for the composite bar BC.
AA,min=
mm²
unanswered
42 answers
2, 0.5*rho*g*A
3. 3/4*rho*g*A*L
q1_2_2 -800, -300, 0, 700
in q1_2_1: 300 is wrong for me, is there maybe a -300?
Q1_1_1
rho*g*A
3/2*rho*g*A
Q1_2_1
400
500
700
565.685424
Q1_2_2
-800
-300
0
700
Q1_2_3
((W*1.25)*(5/3*H))/(A_0*E_0)
need the rest...
It is 0.5*rho*g*A as trustee says.
RCx=
incorrect
34⋅ρ⋅g⋅A⋅L
You have used 1 of 3 submissions
Q1_1_3 : 40.0 POINTS
Obtain a symbolic expression for the axial force in the bar N(x) in terms of ρ, g, A, L, x (with ρ written as rho):
for 0≤x<L, N(x)=
unanswered
for L<x≤3L, N(x)=
unanswered
You have used 0 of 3 submissions
Q1_1_4 : 80.0 POINTS
Obtain symbolic expressions for the maximum tensile and compressive stresses ( σmax,Tn and σmax,Cn )and their locations (coordinates xmax,T and xmax,C ) in terms of ρ, g, L (with ρ written as rho). (Note: enter the expressions for the stresses with their appropriate signs.)
σmax,Tn=
unanswered
at location xmax,T=
unanswered
σmax,Cn=
unanswered
at location xmax,C=
unanswered
You have used 0 of 3 submissions
Q1_1_5 : 60.0 POINTS
Obtain a symbolic expression for the displacement ux(x=2L) in terms of ρ, g, E, L (with ρ written as rho):
ux(x=2L)=
unanswered
You have used 0 of 3 submissions
rho*g*A
1/2*rho*g*A
Q.1_1_2
-2*rho*g*A*L
0<x<L
rho*g*A*(L-x)
L<x<3L
(rho*g*A)/2*(L-x)
SERIOUS ANSWERS NEEDED
Use the force method for statically indeterminate structures to obtain a symbolic expression for the reaction RCx at the support C in terms of ρ, g, A, L (with ρ written as rho):
Obtain symbolic expressions for the maximum tensile and compressive stresses ( σmax,Tn and σmax,Cn )and their locations (coordinates xmax,T and xmax,C ) in terms of ρ, g, L (with ρ written as rho). (Note: enter the expressions for the stresses with their appropriate signs.)
σmax,Tn=
unanswered
at location xmax,T=
unanswered
σmax,Cn=
unanswered
at location xmax,C=
unanswered
Obtain a symbolic expression for the displacement ux(x=2L) in terms of ρ, g, E, L (with ρ written as rho):
ux(x=2L)=
unanswered
(3*g*L^2*rho)/(8*E)
Use the force method for statically indeterminate structures to obtain a symbolic expression for the reaction RCx at the support C in terms of ρ, g, A, L (with ρ written as rho):
Obtain symbolic expressions for the maximum tensile and compressive stresses ( σmax,Tn and σmax,Cn )and their locations (coordinates xmax,T and xmax,C ) in terms of ρ, g, L (with ρ written as rho). (Note: enter the expressions for the stresses with their appropriate signs.)
-A*g*L*rho
Obtain symbolic expressions for the maximum tensile and compressive stresses ( σmax,Tn and σmax,Cn )and their locations (coordinates xmax,T and xmax,C ) in terms of ρ, g, L (with ρ written as rho). (Note: enter the expressions for the stresses with their appropriate signs.)
σmax,Tn=
unanswered
at location xmax,T=
unanswered
σmax,Cn=
unanswered
at location xmax,C=
unanswered
I only have the locations
T=0
C= 3*L
σmax,Tn=
unanswered
at location xmax,T=
unanswered
σmax,Cn=
unanswered
at location xmax,C=
unanswered
at location xmax,T= 0
σmax,Cn= -g*L*rho
at location xmax,C= 3*L
my contribution :D have a nice day
400
500
699.99
665.68
0 answers