Q1 A four noded one dimensional \'truss\', shown below is to be analysed using t
ID: 1732813 • Letter: Q
Question
Q1 A four noded one dimensional 'truss', shown below is to be analysed using the direct stiffness method (G Nooles1 The truss members are made from reinforced concrete with the following section properties Econcrete 30 GPa; Esteel 200 GPa Bar Cross section reinforcement 4 200 X 200 mm 300 X 300 mm 200 X 150 mm 300 X 300 mm 100 X 150 mm 200 X 300 mm 4 3.5 4 If the externally applied forces are of magnitude Fi1 7 kN and F2 -6 kN Calculate a) b) the reaction forces the stresses and strains in each member Assuming the reinforcing steel remains fully bonded to the concrete, determine if any members would crack (take f 3 MPa)Explanation / Answer
A1=40000
A2=90000
A3=30000
A4=90000
A5=15000
A6=60000
Econcrete =30Gpa
Esteel =200Gpa
F1=7KN
F2=6KN
REACTIONS :-
member 1:-
RB×12=7×2×1
RB =1.16KN
RA+RB=7KN
RA=7-1.16
=8.83KN
MEMBER 2:-
RB×4=7×2×1
RB =3.5KN
RA =7-3.5
=3.5KN
MEMBER 3:-
RB×8=7×4×2
=7KN
RA=0KN
MEMBER 4:-
RB×5=6×2×1
RB =2.4KN
RA =6-2.4
=3.6KN
MEMBER5 :-
RB×3=6×1.5×0.75
=2.20KN
RA=6-2.25
=3.7KN
STRESS =load ÷area
Member1=7÷40000
=1.75×10^-4N/MM^2
Member 2=6÷90000
=6.67×10^-5N/MM^2
Member 3:-
Where load=stress area
6.67×10^-5×30000
=2.001
Where 2.001 ÷30000
=6.67×10^-5N/mm^2
Member4:-
6.67×10^-5×90000
=6.003
Where 6.003÷90000
=6.67×10^-5
Member5;-
6.67×10^-5×15000
=4.46
Where 4.46÷15000
=2.96×10^-13N/mm^2
Members 6;-
6.67×10^-5×60000
=4.002
Where
4.002÷60000
=6.67×10^-5N/mm^2
STRAIN =changeing length ÷original length
Members 1:-2÷12=0.16
Members2:-2÷4=0.5
Members 3:-4÷8=0.5
Members 4:-2÷5=0.4
Members 5:-1.5÷3=0.5
Members 6:-3÷9=0.33
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