1. Given the figure below, • calculate the reactions, • derive equations for shear and moment • draw...

Question

1. Given the figure below, • calculate the reactions, • derive equations for shear and moment • draw the complete shearing force and moment diagrams, • and determine the magnitude and location of the maximum absolute value of the shearing force and bending moment.
8 k/ft.
5 ft.
5ft.
5 ft.
A,
k means 1,000 pounds
By
2. Given the figure below, • calculate the reactions. • derive equations for shear and moment • draw the complete shearing force and moment diagrams, • and determine the magnitude and location of the maximum absolute value of the shearing force and bending moment.
10 k/ft
13,
5k/ft

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David · Accepted Answer

Solutions
Q1-Answer
As per given information in question, we have 
Reaction forces
Now we can calculate reaction forces after converting above diagram in to free body diagram.
As we may see in free body diagram that this is symmetrical loading  
∑FY = 0
AY + BY = 40000 lb
∑MA = 0
40000 x 7.5 – 15 x BY = 0
BY = 40000 x 7.5 /15 = 20000 lb
BY = 20000 lb
AY = 20000 lb
Shear and moment equation and diagram-
                          X
AC= CD=DB= 5 ft
Let a section XX at a distance X from point A
Shear force-
Shear force, for AC, x= 0 
FAC= AY =20000 lb
Shear force for CD, FCD = AY – 8000 (X-5)
Where, X= 5 ft to X= 10 ft
At point C, x = 5 ft
Hence,
FC = AY – 8000 (5-5) = 20000 lb
At point D, x = 10 ft
Hence,
FD = AY – 8000 (10-5) = 20000 – 40000 = -20000 
FD = -20000 lb
For DB,
FDB= -2000 lb
Hence, shear force diagram
Bending moment diagram
We have displayed bending moment diagram as mentioned above.
For AC
BM, MAC= AY. X
At point A 
BM, MA= 0 because X=0
At point C
BM, MC= 20000 x 5 =100000 lb-ft 
For CD
BM, MCD= AY. X – 8000(X-5) (X-5)/2
Where, X= 5 ft to X= 10 ft
Hence, at point C, X= 5 ft
MC= 20000 x 5 =100000 lb-ft
Hence, at point D, X= 10 ft
MD= 20000 x 10 – 8000 x 25/2 = 100000 lb-ft
MD= 100000 lb-ft
We have to also find here the location of maximum bending moment
 For maximum bending moment, shear force will be zero
We will find the location, where shear force is zero
 AY – 8000 (X-5) =0
20000 – 8000 (X-5) =0
20000 = 8000 (X-5) 
(X-5) = 2.5
X= 7.5 ft
So we will find the maximum value of BM at point X = 7.5
So, maximum bending moment 
M Max = AY. X – 8000(X-5) (X-5)/2
M Max = 20000 x 7.5 – 8000(7.5-5) (7.5-5)/2
M Max = 125000
For DB-
Bending moment 
MDB= 20000.

1. Given the figure below, • calculate the reactions, • derive equations for shear and moment • draw the complete shearing force and moment diagrams, • and determine the magnitude and location of the...

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