Structural Analysis and Design: Bending Moments and Shear Forces

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Bending moments and shear forces with
beam design considerations
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Table of Contents
Task 1:.................................................................................................................................3
Task 1 (a).........................................................................................................................3
Problem No.1-A...........................................................................................................3
Problem No.1-B...............................................................................................................6
Problem No. 1-C..............................................................................................................9
Problem No. 1-D............................................................................................................12
Problem No.1-E.............................................................................................................15
Task (B).........................................................................................................................17
Task 1(C).......................................................................................................................18
Task 1(D).......................................................................................................................19
Task 2:...............................................................................................................................22
Task-2 (A)......................................................................................................................22
Problem-a...................................................................................................................22
Problem b.......................................................................................................................24
Problem c.......................................................................................................................27
Problem d.......................................................................................................................30
Problem e.......................................................................................................................33
Task 2(B).......................................................................................................................34
Task 2(C).......................................................................................................................35
Task 2(D).......................................................................................................................36
Task 3:...............................................................................................................................37
Task 3(A).......................................................................................................................37
Task 3(B).......................................................................................................................37
Task 3(C).......................................................................................................................38
Task 4:...............................................................................................................................39
Task 4(C).......................................................................................................................42
Task 4(D).......................................................................................................................42
References:........................................................................................................................44

List of Figures
Figure 1: Beam arrangements..............................................................................................3
Figure 2: Shear force and bending moment.........................................................................5
Figure 3 Beam arrangement.................................................................................................7
Figure 4: Shear force and bending moment.........................................................................9
Figure 5: Beam arrangement.............................................................................................10
Figure 6 Shear force and bending moment........................................................................12
Figure 7: Beam arrangement.............................................................................................13
Figure 8: Shear force and bending moment.......................................................................15
Figure 9 Beam arrangement...............................................................................................16
Figure 10 : Shear force and bending moment....................................................................18
Figure 1 Safety requirements in structural designs............................................................19
Figure 2 Safer steel beam selection...................................................................................21
Figure 11: Beam arrangement...........................................................................................23
Figure 12 : Beam arrangement..........................................................................................25
Figure 13 Beam arrangement.............................................................................................28
Figure 14: Beam arrangement...........................................................................................31
Figure 15: Beam arrangement...........................................................................................34
Figure 3 Deformation in a beam structure.........................................................................35
Figure 16: Height calculation diagram..............................................................................42
List of Tables
Table 1 Slenderness ratio analysis in structures................................................................39

Task 1:
Task 1 (a)
Problem No.1-A
A simply supported beam with a span of 14m is subjected to a point load of 150KN at the
midpoint. Draw the beam arrangement and determine the reactions at the supports. Calculate and
draw the shear force diagram and the bending moment diagram running along the beam.
Problem solution
Stated data
Spanlength=l=14 m
Point load =150 KN
Figure 1: Beam arrangements
To find out
Reaction Forces at point A∧B=R A∧RB=?
Bending Moment of beams=B . M =?
Shear Force of beams=S . F=?
Finding the Reaction forces RA ∧RB
For equilibrium beam we know
1. summation of all the rising forces=summation of all the downhill forces
2. Summationof all moments=0

RA +RB =150 KN
The moment at point A
RB .14=150. 7
14. RB =1050
14 . RB =1050
RB= 1050
14 =75 KN
Inducting the value of RB in RA +RB =150 KN
RA =150 KN−70 KN =75 KN
Finding the bending moment
At Point A
(B . M )A=0
At point B
(B . M )B =0
At Point C
( B . M )C=R A . L
2
( B . M )C= W
2 . L
2
( B . M )C= W . L
4
( B . M )C=(150.14)
4 =525 KN . m
Finding the shear forces
At point A
( S . F ) A =W /2
( S . F ) A =150
2 =75 KN

At Point B
( S . F ) B =W /2
( S . F ) B = W
2 −W
2 =0
At point C
( S . F ) c= W
2 −W =−W
2
( S . F ) c=−W
2
( S . F )c=−150
2 =−75 KN
Figure 2: Shear force and bending moment

Problem No.1-B
Problem solution
Stated data
Point load =65 KN
Spanlength=l=8 m
Figure 3 Beam arrangement
To find out
Reaction Forces at point A∧B=R A∧RB=?
Bending Moment at point A , B∧C=B . M=?
Shear Force at point A , B∧C=S . F=?
Finding the Reaction forces RA ∧RB
RA is given by
RA = W .b
l
RA = 65.6
8 =48.75 KN
And RB is given by
RB= W . a
l
RB= 65.2
8 =16.25 KN
Finding the bending moment
B.M at Point A

( B . M . ) A =0
B.M at Point B
( B . M . )B =0
B.M at Point C
( B . M . )C=RA . a
As we know RA = W × b
l ,
( B . M . )C=(W . b
l )(a)
Inducting the values of variables give us,
( B . M . )C= (65 X 6
8 ) ( 2 )=97.5 KN . m
Finding the shear forces
Shear force at Point A
( S . F . ) A =W . b
l
Inducting the value of variables give us,
( S . F . ) A =(65)(6)
8 =48.75 KN
Shear force at Point B
( S . F . ) B =W . a
l − W . a
l =0
Shear force at Point C
( S . F . )C= W . b
l −W
( S . F . ) C=W [ ( b /l ) −1 ]
( S . F . )C=W [ b−l/l ]
( S . F . )C=−W [ l−b /l ]

We know that
l−a=b
a+b=l
So,
( S . F . )C=−W . a
l
Inducting the value of variables in equation gives us,
( S . F . ) C=− ( 65 ) ( 2 )
8 =−16.25 KN
W =65 KN

Figure 4: Shear force and bending moment

Problem No. 1-C
Problem solution
Stated data
Uniformly Distributed load=UDL=25 KN
l=25 m
Spanlength=l=25 m
Figure 5: Beam arrangement
To find out
Downward∧upward reaction Forces=RA ∧RB =?
Bending Moment at point A , B∧C=B . M=?
Shear Force at point A , B∧C=S . F=?
Finding the Reaction forces RA ∧RB
The equilibrium beam
We know that,
1. summation of all therising forces=∑ of all the downhill forces
2. Summationof all moments=0
RA + RB =25× 25=625 KN
25. RB = ( 25 ×25 ) ( 25
2 ) =312.5 KN
So , RB=312.5 KN
Inducting value of RB in equation gives us,
RA =625−312.5=312.5 KN
Finding the bending moment
Shear force equals to zero gives the maximum bending value