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...

...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...

...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...

...for reactions, shear force 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...

...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:...

...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...

...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...

...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...

...
Bending in beams
Key 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....

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