eng1201 tutorial 10 problem set (Set No. 6)
1. Calculate the area A, the location of the neutral axis, and the second moment of area (cross section stiffness) IXX for each of the following shapes, and rank them in order of increasing stiffness. Scale the dimensions from the drawings, and work in mm. For a circle,

π r4 I= . 4

X X X (b) (a) X (d)

X X X

X

(c)

X X X X X

X

(e)

(f)

(g)

X

X X

X X

X

(h) (i)

(j)

2

2. A rectangular beam with a cross section 200 mm x 100 mm spans 6 metres and carries a uniform load of 2 kN/m. a) Calculate the reactions. b) Draw the shear force and bending moment diagrams. c) Calculate I for the cross section, about the axis of bending. d) Calculate the maximum compressive stress in the beam, and show where it occurs along the length, and on the cross section. e) Calculate the maximum tensile stress in the beam, and show where it occurs along the length, and on the cross section.

2 kN/m

6 metres

3. The machine component shown below can be analysed as an overhung simply supported beam. It is made of cast iron, which is much stronger in compression than in tension. If the maximum stress must be limited to 30 MPa in tension and 100 MPa in compression, calculate the maximum value of the load P that can be applied.

200 50 200

P

50 cross section dimensions in mm 0.5 m

1.0 m

3

4. Calculate the maximum stress in a beam which has the cross section drawn below. It is subjected to a moment about the YY axis of 20 kN-m (top of the beam in compression). Is the maximum stress tensile or compressive?

50

200

50

Y 200
dimensions in mm

Y 40

5. Two 50 mm by 150 mm wooden planks are glued together to form a T section as shown in the figure below. If a bending moment of 5 kNm is applied to the beam acting around a horizontal axis (top in compression), a) Find the stresses at the extreme fibres. b) Calculate the total compressive force developed by the...

...MEM23061A Test Mechanical Engineering Materials
Lab. BEAM BENDING
The bending of beams is one of the most important types of stress in engineering. Bending is more likely to be a critical stress than other types of stress - like tension, compression etc.
In this laboratory, we will be determining the Modulus of Elasticity E (also called Young's Modulus) of the various materials and using Solid Edge to determine the SecondMoment of Area for the different cross-sections.
[pic]
Equations
Use units: Force (N), Length (mm), Stress (MPa)
E = Young's Modulus or Mod of Elasticity (MPa)
I = 2nd Moment of Area or AreaMoment (mm4). Can calculate using SolidEdge sketch.
BENDING
[pic]
In our case, we must first convert the mass to Newtons (N). W = kg * 9.81
L is the span length in (mm).
I is the SecondMoment of Area in (mm4). We can calculate this for a rectangle using a simple formula;
[pic]
For other shapes it is not so simple. We need to calculate these using a program such as Solid Edge (see below).
Determining the value of E in MPa. From the above equation,
Deflection z = W * L3 / (48 * E * I)
so E = W * L3 / (48 * z * I)
Determining Stress in MPa. From the above equation,
Bending Moment (Nmm) M = W*L / 4 ...

...disease or infirmity." An important consequence of this definition is that mental health is described as more than the absence of mental disorders or disabilities. Also, mental health is a state of well-being in which an individual realizes his or her own abilities and improve their cognitive, can cope with the normal stresses of life, can work productively and is able to make a contribution to his or her community. In this positive sense, mental health is the foundation for individual well-being and the effective functioning of a community. Accordingly I am developing my state of mental health from the time I came to Malaysia to study all by myself, because, I learnt many things in my life after I came to Malaysia and I was able to go through stress with a positive mind even
though I was all alone by myself. Further, multiple social, psychological, and biological factors determine the level of mental health of a person at any point of time. For example, persistent socio-economic pressures are recognized risks to mental health for individuals and communities. The clearest evidence is associated with indicators of poverty, including low levels of education. Poor mental health is also associated with rapid social change, stressful work conditions, gender discrimination, social exclusion, unhealthy lifestyle, risks of violence and physical ill-health and human rights violations. There are also specific psychological and personality factors that make people...

...and moment for:
a. Simply supported beam
b. Simply supported beam with one end overhanging
c. Simply supported beam with both ends overhanging.
2. To calculate shear force and moment using influence line
3. To determine maximum shear force and moment
4. Calculate Absolute MaximumMoment (MMM)
4.1 INTRODUCTIONS:
Influence line is to:
Analysis a structure due to moving load along the beam.
Show the changes in reaction, shear stress, moment and displacement in certain point in structure when applied a unit load.
Determine the greatest position the greatest value of live load in beam.
4.2 DIFFERENCES BETWEEN INFLUENCE LINE DIAGRAM (ILD) AND BMD (BENDING MOMENT DIAGRAM)
INFLUENCE LINE DIAGRAM
(ILD)
BENDING MOMENT DIAGRAM (BMD)
a) Static and Moving Load
b) Diagrams show only one point on the beam.
c) Calculations based on the virtual load.
d) Straight line only
e) Calculations do not refer to reactions of beam.
f) Unit: m
a) Static load only.
b) Diagram shows the moment at all points on the beam.
c) Calculations based on real loads.
d) Straight lines and curves.
e) Calculations based on the SFD.
f) Unit : kNm
4.3 BASIC CONCEPT TO DRAW INFLUENCE LINE DIAGRAM (ILD)
1 unit
x
A B C
a b
RAY = [L-x]/L 1-x/L RCY=x/L
4.3.1 REACTION
ILD RAY L/L
b/L
[+]...

...EXPERIMENT : CONTINUOUS BEAM
1.0 Learning outcome:
1.1 Determine the magnitude of the fixing moment in a continuous beam by experiment and
to compare this with the value predicted by theory.
2.0 Apparatus/Equipment:
2.1 Aluminium
2.2 Brounze
2.3 Weight
2.4 Dial gauge
Weight Dial gauge Aluminium Brounze
3.0 Safety and health:
3.1 Make sure the student follow the laboratory or workshop safety regulator.
3.2 Experiment must be conduct by lecturers or experience lab assistance.
3.3 Always wear appropriate protective clothing.
3.4 Be familiar with the location of emergency equipment-fire alam ,fire
extinguisher,emergency eye wash and safety shower.
3.5 Always wash hand and arms wit soap and water before leaving the work area.
3.6 Never perform unauthorized work,preparation or experiments.
4.0 Theory:
1.Horizontal structural member used to support horizontal loads such as floors, roofs, and decks.
2. Consider a simply supported beam of length, L.
3. The The cross section is rectangular with width b and height h cross section is rectangular, with width, b, and height, h.
4. Beams have been used since dim antiquity to support loads over empty space, as roof beams supported by thick columns, or er of the approximate methods...

...1.0 OBJECTIVE
1.1 To examine how bending moment varies with an increasing point load.
1.2 To examine how bending moment varies at the cut position of the beam for various loading condition.
2.0 LEARNING OUTCOMES
2.1 To application the engineering knowledge in practical application
2.2 To enhance technical competency in structural engineering through laboratory application.
2.3 To communicate effectively in group.
2.4 To identify problem, solving and finding out appropriate solution through laboratory application.
3.0 THEORY
3.1 There are a number of assumptions that were made in order to develop the Elastic Theory of Bending. These are:
* The beam has a constant, prismatic cross-section and is constructed of a flexible, homogenous material that has the same Modulus of Elasticity in both tension and compression (shortens or elongates equally for same stress).
* The material is linearly elastic; the relationship between the stress and strain is directly proportional.
* The beam material is not stressed past its proportional limit.
* A plane section within the beam before bending remains a plane after bending (see AB & CD in the image below).
* The neutral plane of a beam is a plane whose length is unchanged by the beam's deformation. This plane passes through the centroid of the cross-section.
3.2 In order to visualize this, think of a black...

...Zuleika Rodriguez
Professor Alan Schlechter/ Daniel Lerner (Nick Jensen)
The Science of Happiness
October 1, 2014
The Moment of Change
Faith, courage and willpower are some values that have shaped me into the character that I am today. Following upon the numerous and impacting conflicts I had throughout my life, I can recall my family reunion last summer. In a quote from Ralph Waldo Emerson, he states, “Be an opener of doors for such as come after thee, and do not try to make the universe a blind alley”. Who would know that those words would somehow apply to me in a rolling whirlwind of uncontrollable events? As I peruse The Brain That Changes Itself by Norman Doidge, I noted that the chapters of Pain, Imagination, and, Turning out Ghosts into Ancestors somehow retold my story of my family reunion last summer.
As the hot summer day had started, I felt the warmth and love from my family that I had not seen for such a long time. We prepared for a big trip to go to a beach resort. At first, I was full of excitement when I heard the great amenities that the resort provided. However, my fear of drowning in the vast ocean had become an overwhelming fear that had developed throughout my life. It was a taunting constant reminder of how afraid I was to lose control, trust myself, and rely on others for help. Nevertheless, even if I learned how to swim, would I still be in this never-ending fear? With many years of struggle, this is what I wanted to...

...Points: 1. Internal bending moment causes beam to deform. 2. For this case, top fibers in compression, bottom in tension.
Bending in beams
Key Points: 1. Neutral surface – no change in length. 2. Neutral Axis – Line of intersection of neutral surface with the transverse section. 3. All cross-sections remain plane and perpendicular to longitudinal axis.
Bending in beams
Key Points: 1. Bending moment causes beam to deform. 2. X = longitudinal axis 3. Y = axis of symmetry 4. Neutral surface – does not undergo a change in length
Consider the simply supported beam below:
Bending Stress in beams
Radius of Curvature, R
P
A Neutral Surface B
Deflected Shape
RA
M M
M
M
RB
What stresses are generated within, due to bending?
Axial Stress Due to Bending:
M=Bending Moment
σx (Compression)
M
Neutral Surface
M
Beam
σx=0 σx (Tension)
stress generated due to bending:
σx is NOT UNIFORM through
the section depth
σx DEPENDS ON:
(i) Bending Moment, M (ii) Geometry of Cross-section
Bending Stress in beams
Bending Stress in beams
Stresses due to bending
R N’ E B’ A’ C’ N’ F D’ Strain in layer EF
y = R
Stress _ in _ the _ layer _ EF E= Strain _ in _ the _ layer _ EF σ E= € ⎛ y ⎞ ⎜ ⎟ ⎝ R ⎠
σ E = y R
€
E σ= y R
Neutral axis
dA dy y N A
€...

...Bending Moment
EXPERIMENT 2B: SHEAR FORCE AND BENDING MOMENT
1. ABSTRACT
Performance-based design approach, demands a thorough understanding of axial forces.
Bending characterizes the behavior of a slender structural element subjected to an
external load applied perpendicularly to a longitudinal axis of the element. By this experiment
we can verify the limit load for the beam of rectangular cross-section under pure bending.
Moments at the specific points are calculated by the method of statics or by multiplying the
perpendicular force or load and the respective distance of that load from the pivot point.
2. OBJECTIVE
The objective of this experiment is to compare the theoretical internal moment with the
measured bending moment for a beam under various loads.
3. KEYWORDS
Bending moment, hogging, sagging, Datum value, under-slung spring, spring balance and
Beam, Neutral axis.
4.
THEORY
Bending Moments:
Bending Moment at AA is defined as the algebraic sum of the moments about the section of all
forces acting on either side of the section.
Definition of a Beam:
Members that are slender and support loadings that are applied perpendicular to their
Page 1 of 14
Bending Moment
longitudinal axis are called beams. Beams are important structural and mechanical elements in
engineering. Beams are in general,...

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