Structural Design Principles: Beam and Column Analysis

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Bending Moments & Shear
Forces with Beam Design
Considerations
Using Principles of Structural
Design
University name
Bending Moments & Shear
Forces with Beam Design
ConsiderationsUsing Principles of Structural
Design.
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Students name:
9/2019/July

Table of Contents
T-(1) Bending moments and shear force supported steel beams solution by calculations and
diagram...........................................................................................................................................3
Determination of the beam arrangement the reaction forces at support-T1(a)............................3
Shear Force and Bending Moment diagrams.........................................................................5
Determination of the beam arrangement the reaction forces at both support-T1(b)...................6
Shear Force and Bending Moment diagrams.........................................................................9
Determination of the beam arrangement, the reaction forces and shear forces at a support-
T1(c)..........................................................................................................................................10
Shear Force and Bending Moment diagrams.......................................................................12
Determination of the beam arrangement, the reaction forces and shear forces at a support for a
uniformly distributed load-T1(d)...............................................................................................13
Shear Force and Bending Moment diagrams.......................................................................15
Determination of the beam arrangement, the reaction forces and shear forces at a support for
an additional point load-T1(e)...................................................................................................16
Shear Force and Bending Moment diagrams.......................................................................18
Safety assurance in designing structures discussing the statuary requirements-T1 (B)............18
Description and examination of producing valid factors in case of live, dead and imposed
loads utilizing the building regulations-T1 (C).........................................................................19
Factors Effect Safety features.............................................................................................19
An example can best explain it..............................................................................................20
Solution..................................................................................................................................20
Selection of Steel beam by using maximum bending moments and existing programs of
practice having a proper examination of economics and safety-T1 (D).............................21
T-(2) Governing the deflection in a simply supported beam when there are both point loads
and uniformly distributed loads.................................................................................................22

Simply supported beam’s deflection determination In problem 1 all parts-T2(a).....................22
Determination of the beam arrangement the reaction forces at support-(a)..............................22
Determination of the beam arrangement the reaction forces at support-(b)..............................25
Determination of the beam arrangement the reaction forces at support-(c)..............................28
Determination of the beam arrangement the reaction forces at support-(d)..............................31
Determination of the beam arrangement the reaction forces at support-(e)..............................34
Mechanical stability affecting Deflection in Beam-T2 (B).......................................................36
Examination of support structures in steel and reinforced structures-T2 (B)............................37
Most effective support system in practically used supports-T2 (D)..........................................38
T-(3) Governing the axial load having a volume of steel and reinforced columns................38
Determination of the axial load capacity of certain value –T3 (a)............................................38
Comparison and exploration of Steel and reinforced columns using slenderness ratio and the
effective length-T3 (A)..............................................................................................................39
Properties of Equipment Used for columns and beams in a fixed structure-T3 (C)..................39
T-(4) Governing the DESIGN solution including the BEAM design and the COLUMN
design............................................................................................................................................40
Determination of the Steel and reinforced concrete solutions by identifying their costs for both
beams and columns –T4 (a).......................................................................................................40
Alternative solution to a reinforced and steel material for attaining a strategic solution- T4 (C)
...................................................................................................................................................43
Building information modelling usage in construction of precise structural design information-
T4 (D)........................................................................................................................................43
List of Tables
Table 1: Slenderness ratio analysis................................................................................................44

List of Figures
Figure 1: Reaction forces length and support..................................................................................4
Figure 2: Reaction forces diagrams.................................................................................................6
Figure 3: Reaction forces spam length and point load....................................................................7
Figure 4: Reaction forces solution showing the bending diagrams...............................................10
Figure 5: Reaction forces uniformly distributed length.................................................................11
Figure 6: Reaction forces shear and bending figures.....................................................................13
Figure 7: Reaction forces udl and length.......................................................................................14
Figure 8: Reaction forces bending and shear figures.....................................................................16
Figure 9: Reaction forces length and udl figure............................................................................17
Figure 10: Reaction forces bended and sheared forces.................................................................19
Figure 11: A floor system carrying a support and load.................................................................21
Figure 12: governing load with a support......................................................................................22
Figure 13: Support system diagram...............................................................................................23
Figure 14: Beam arrangement.......................................................................................................26
Figure 15: Reaction forces length and support..............................................................................29
Figure 16: Reaction forces udl diagram.........................................................................................32
Figure 17: Reaction forces support system....................................................................................35
Figure 18: Support structures in a steel and concrete....................................................................38
Figure 19: concrete solutions of a support system.........................................................................43

T-(1) Bending moments and shear force maintained steel beams
solution by calculations and diagram
Determination of the beam arrangement the reaction forces at support-T1(a)
Given data
Point load at midpoint= 150KN
Spam length= 14m
Figure 1 Reaction forces length and support
Required data
Shear Forces=?
Bending Moments=?
Reaction Forces=R A ∧RB =?
Shear forces calculation
S.F On point “A”
S . F=(W )
2 =¿)¿ 75 kN
S.F On point “B”

S . F=( W
2 )=−( W
2 )+(W
2 )=zero
S.F On point “C”
S . F=( W
2 )−(W )=−( W
2 )=−( 150
2 )
S . F=−75 kN
Reaction Forces
When the beam is in equilibrium
a) addition of all theupwad forces=addition of all thedownward forces
RA + RB =150 KN _______________________ (1)
b) additionof all themoment forces=zero
Moment At point A
(R¿¿ B ×14)−(150 ×7)=0 ¿
(14 RB−1050)=0
14 RB=1050
RB=(1050/14)
RB=75 kN
Put the value of RB in eq#1
RA + 75 kN=150 kN
RA =150 kN −70 kN
RA =75 kN
Shear Force and Bending Moment diagrams

Figure 2Reaction forces diagrams
Determination of the beam arrangement the reaction forces at both support-T1(b)
Given data

Point load at left side= 6kN
Spam length= 8m
Figure 3Reaction forces spam length and point load
Required data
Shear Forces=?
Bending Moments=?
Reaction Forces=R A ∧RB =?
Shear forces calculation
S.F On point “A”
S . F=(W × b)
l
Put the values of l, W and b in the equation as given
S . F=(65× 6)
8 =48.75 kN
S.F On point “B”
S . F=−( W ×a
l )+( W ×a
l )=zero

S.F On point “C”
S . F=( W × b
l )−(W )=W [ ( b
l )−1 ] =W [ b−l
l ]=−W [ l−b
l ]
the length is,
L=a+b
Put the value of length in the derived equation. It will then become
S . F=−( W∗a
l )
Then Put the values we have in the derived above equation, it will be then
¿−( 65∗2
8 )
S . F=−16.25
Bending Moment Calculations
B.M on point “A”
BM =zero
B.M on point “C”
BM =( R¿¿ A)∗a ¿
As, ¿ ¿ ) then it will become
BM =( W . b
l )∗a
Put the values WE have in the equation above, it will then become
BM =( 65.6
8 )×2=97.5 kN . m

B.M on point “B”
BM =zero
Reaction Forces
At Point A
RA =¿)
RA =¿)
RA =48.75 kN
At Point B
RB=¿)
RB= 65 ×2
8
RB=16.25 kN

Shear Force and Bending Moment diagrams
Figure 4Reaction forces solution showing the bending diagrams

Determination of the beam arrangement, the reaction forces and shear forces at a
support-T1(c)
Given data
Uniformly distributed load= 25kN
Spam length= 25m
Figure 5Reaction forces uniformly distributed length
Required data
Shear Forces=?
Bending Moments=?
Reaction Forces=R A ∧RB =?
Shear Forces
Shear forces on point “B”
SF=W ×l
2 = 25 ×25
2 =312.5 KN
Shear forces on point “C”
SF=−W × l
2 + W ×l
2 =zero
Shear forces on point “A”
SF=−W × l
2 =−25 × 25
2 =−312.5 KN