Using singularity functions, write the equations for the shear and bending moment for the beam
and loading shown. Use MATLAB to write a code to plot the shear and bending moment
diagrams. Determine the maximum value of the bending moment In the beam from your
MATLAB plot. Using singularity functions, write the equations for the shear and bending
moment for the beam and loading shown. Use MATLAB to write a code to plot the shear and
bending moment diagrams. Determine the maximum value of the bending moment in the beam
from your MATLAB plot.
Solution
due to symmetry
reaction at each support= 3*3+8/2= 13 kips
for 0<=x<=3 ft
SF= RA - 3*x= 13 - 3*x
for 3<=x<=7 ft
SF= 13-9= 4 kifs
for 7<=x<=11 ft
SF = 4-8=-4 kips
for 11<=x<=14 ft
sf= -4 -3*(x-11) kips
BM
for 0<=x<=3 ft
BM= RA*x-3*x2/2 = 13*x-1.5*x2
for 3<=x<=7 ft
BM= 13*x-9*(x-1.5)
for 7<=x<=11 ft
BM= 13*x-9*(x-1.5) -8*(x-7)
for 11<=x<=14 ft
BM
13*x-9*(x-1.5) -8*(x-7) -3*(x-11)2/2
matlab for SF
%MATLAB FOR SF
subplot(1,2,1)
hold on
for i= 0:0.5:14
if i<=3
sf=13-3*i;
ealsif i<=7
sf=4;
ealsif i<=11
sf=-4;
eals
sf= -4-3*(i-11);
end
plot(i,sf,\'*\')
end
xlabel(\'x\')
ylabel(\'SF\')
hold off
%MATLAB FOR BM
subplot(1,2,2)
hold on
for i= 0:0.5:14
if i<=3
BM=13*i-3*i^2/2;
ealsif i<=7
sf=13*i-9*(i-1.5);
ealsif i<=11
sf=13*i-9*(i-1.5)-8*(i-7);
eals
sf= -13.i-9*(i-1.5)-8*(i-7)-3/2*(i-11)^2;
end
plot(i,BM,\'*\')
end
xlabel(\'x\')
ylabel(\'BM\')
hold off.
Using source combination to first simplify the circuit, determine the.pdf
1. Using source combination to first simplify the circuit, determine the power dissipated by the 5.8
k Ohm resistor in the circuit shown. Express your answers to four significant figures.
Solution
Using Super postion theorem we can solve this problem
current through 5.8Kohm due to 1mA current source alone:
I5.8kohm_1mA=1mA*(4.7K/(4.7k+5.8k)
=1mA*4.7/10.5
I5.8kohm_1mA =0.447mA
current through 5.8Kohm due to 2mA current source alone:
I5.8kohm_2mA=2mA*(4.7K/(4.7k+5.8k)
=2mA*4.7/10.5
I5.8kohm_2mA=0.895mA
current through 5.8Kohm I5.8kohm=0.89mA+0.447mA=1.342mA
Power due to 5.8kohm resitance
P5.8kohm=(1.342mA)2 *5.8kohm
P5.8kohm=10.44mW
