Beam Assignment Solutions
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7/30/2019 Beam Assignment Solutions
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7.2 kN
Shear
Force
Bending
Moments
0
3.6 kN
-3.6 kN
0
13.32 kN.m
-13.32 kN.m
13.32 kN.m
3.7 m 3.7 m
3.6 kN 3.6 kN
3.6 kN
=3V
2A
=3 3.6 103 N
2 89 mm 300 mm
= 0.202 MPa
c = 150 mm
= McI
=13.32 106 N mm 150 mm
89 (300)3 /12 mm4
= 9.98 MPa
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5.6 m
A B
4.7 kN/m
RA = RB =5.6 4.7
2= 13.16 kN
Fy = 13.16 V
= 0
V = 13.16 kN
Fy = 13.16 26.32 V
= 0
V = 13.16 kN
13.16 2.8/2 = 18.424 kN m18.424 18.424 = 0
5.6 m
Shear
Force
Bending
Moments
0
13.16 kN
-13.16 kN
0
18.424 kN.m
4.7 kN/m
13.16 kN 13.16 kN
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13.16 kN x = 0 m x = 5.6 m
=3V
2A
=3 13.16 103 N
2 89 mm 335 mm
= 0.662 MPa
18.424 kN mc = 335/2 = 167.5 mm
=Mc
I
=18.424 106 N mm 167.5 mm
89 (335)3 /12 mm4
= 11.1 MPa
2.3 m
4.6 kN
10 kN/m
A B
1.15 m
4.6 kN
AB
23.0 kN
Ma
RA
1.15 m
Fy = RA 23.0 4.6
= 0
RA = 27.6 kN
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MA = Ma 23.0 1.15 4.6 2.3
= 0
Ma = 37.03 kN m
A
37.03
kN.m
27.6 kN
V M
Section right of A
A37.03
kN.m
27.6 kN
V M
Section left of B
23 kN1.15 m 1.15 m B
Fy = 27.6 V
= 0
V = 27.6 kN
Msection = M + 37.03
= 0
M = 37.03 kN m
Fy = 27.6 23 V
= 0
V = 4.6 kN
Msection = M + 37.03 + 23 1.15 27.6 2.3
= 0
M = 0
m =y1 y0
x1 x0
=4.6 27.6
4 0= 10
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y = mx + c = 10x + c cy = 10x + 27.6
M(x) =
(10x + 27.6) dx
= 5x2 + 27.6x + c
=5x2
+27
.6x 37
.03
37.02 kN mM(0) = 37.03 c = 37.03
4.6 kN
AB
27.6 kN
27.6 kN
4.6 kN0
0
-37.03 kN
Shear
Force
Bending
Moment
d = 306 mmI = 177 106 m4 = 177 106 mm4
c = 153 mm 37.03 kN m
B =Mc
I
=
37.03 106 N mm 153 mm
177 106 mm4
= 32.0 MPa
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20 kN
B
40 kN1.0 m2.0 m2.0 m
200 mm
25 mm150 mm
25 mm
A
MA = 40 2 + RB 4 20 5
= 0
RB = 45 kN
MB = RA 4 + 40 2 20 1
= 0RA = 15 kN
(Check) FY = 15 40 + 45 20
= 0
20 kN
C
40 kN1.0 m2.0 m2.0 m
A B
D15 kN 45 kN
15 kN
0
0
20 kN
-25 kN
30 kN.m
-20 kN.m
Shear Force
Bending Moment
y =A1y1 + A2y2
A1 + A2
=(150 25) 12.5 + (25 200) 125
(150 25) + (25 200)
= 76.789 mm
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200 mm
25 mm150 mm
25 mm
CX=76.789 mm
1
2
2x x
2
150 25 76.789 12.5 150(25)3/121 = 3750 = 64.289 = 15.499 106 = 0.19531 106 = 15.694 106
25 200 76.789 125 25(200)3/122 = 5000 = 48.211 = 11.622 106 = 16.667 106 = 28.289 106
= 43.983 106
43.983 106 mm4
C =Mc
I
=30 106 N m 76.789 mm
43.983 106 mm4
= 52.376 106 MPa
B =20 106 N m (225 76.789) mm
43.983 106 mm4
= 67.395 106 MPa
C =Mc
I
=30 106 N m (225 76.789) mm
43.983 106 mm4
= 101.09 106 MPa
B =20 106 N m 76.789 mm
43.983 106 mm4
= 34.918 106 MPa
V = 25 kN
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A =(225 76.789) 25 = 3705.3 mm2 yy =(225 76.789)/2 = 74.106 mm
=VQ
It
=25 103 N 3705.3 mm 74.106 mm
43.983 106 mm4 25 mm
= 6.243 MPa
6.243 MPa
