Essays on Modulus

HW How does the mechanical property of human bone compare to properties of cattle, horse, and pig? (Compare Modulus of Elasticity, Ultimate tensile strength, Ultimate compressive strength for Tibia and femoral bone) The modulus of elasticity of the human femur bone is 17.6 GPa, which is higher than that of the pig-14.9 but lower than that of the cattle-25.0, and horses-25.5 (Pal 30). Similarly, the modulus elasticity of the human tibia bone is 18.4 GPa, which is higher than that of the pig-17.2, but lower than that of the horses-23.8 and cattle-24.5. Explain how many structural layers exist in ...

Introduction

How materials behave is dependent on various factors, some of which include their mechanical properties. When the material experiences various loading conditions, its behavior reflects its mechanical conditions as well as the effect of the loading conditions. When a material experiences various loading conditions, the material experiences either shear stress, tensile strength, or compressive strength. The tensile properties of a material relate to its ability support any axial loads to which it is subjected without rapturing (Department of Engineering. 2007). When a material is subjected to tensile stress, the deformation that occurs is in the form of elongation or ...

Results

Deflection per Unit Load (mm/kN) The following method is used to calculate the deflection per unit load in mm/kN from the slope of the graph. Slope=y2-y1x2-x1=6.41-1.2820.19-0.03=32.05kNmm Deflection=132.05=0.0312mmkN

Strain per Unit Load (µƐ/kN)

The following method is used to calculate the strain per unit load in µƐ/kN from the slope of the graph. For Strain (positive) Slope=y2-y1x2-x1=6.41-1.28242-6=0.142kNμε Strain=1slope=10.142=7.042μεkN

For Strain (negative)

Slope=y2-y1x2-x1=6.41-1.28246-8=0.135kNμε Strain=1slope=10.135=7.407μεkN

Calculations and Discussion

Stress The following method is used to calculate stress per unit load in N/mm2/kN from the strain measurements. Stress=StressLoad=8.61×106-1.23×1066.41-1.282=1.439×106N/mm2kN Stress=StressLoad=9.43×106-1.64×1066.41-1.282=1.519×106N/mm2kN

The following method is used to calculate the theoretical value of maximum stress.

Maximum stress=MomentElastic Modulus Moment=Load×Distance=1kN×378.5mm=378.5 kN.mm Maximum stress=MomentElastic Modulus=378.574.94×10-6=5.05×106N/mm2kN The values of the above ...

Results

Deflection per Unit Load (mm/kN) The deflection per unit load in mm/kN is calculated from the slope of the graph as follows. Slope=RiseRun=y2-y1x2-x1=6.4113-1.282260.2-0.04=32.0565kNmm Deflection per unit load=1slope=132.0565=0.031195mmkN

Strain per Unit Load (µƐ/kN)

The strain per unit load in µƐ/kN is calculated from the slope of the graph as follows. For Strain (+) Slope=RiseRun=y2-y1x2-x1=6.4113-1.2822642-7=0.146544kNμε Strain per unit load=1slope=10.146544=6.8239μεkN

For Strain (-)

Slope=RiseRun=y2-y1x2-x1=6.4113-1.28226-48-(-8)=-0.128226kNμε Strain per unit load=1slope=1-0.128226=7.799μεkN

Calculations and Discussion

Stress The stress per unit load in N/mm2/kN is calculated from the strain measurements as follows. Stress per unit load=StressLoad=8.61×106-1.435×1066.4113-1.28226=1.399×106N/mm2kN Stress per unit load=StressLoad=-9.84×106--1.64×1066.4113-1.28226=-1.599×106N/mm2kN

The theoretical value of maximum stress is calculated as follows.

Theoretical maximum stress=MomentElastic Modulus Moment=Load×Distance=1kN×657.5mm=279 kN.mm Theoretical ...

Q1. A 200mm diameter pipeline divides into two smaller pipelines, one being 100mm in diameter and the other being 150mm in diameter. If the velocity in the 100mm pipe is 0.3m/s and that in the 150mm is 0.6m/s, calculate the flowrate in litres/s and the velocity in m/s in the 200mm pipe. [ 13 l/s, 0.413m/s] Solution: Flow Rate = (pi/4)(0.1)2(0.3) + (pi/4)(0.15)2(0.6) = 0.01296 cubicmeters/sec = 12.96 l/sec. (ans.). Velocity = (Flow Rate)/(Area) = [0.01296]/[(pi/4)(0.1)2] = 0.4125 m/s. Q2. If the specific volume of water is 0.001251 m3 /kg. calculate:

The mass and weight ...

Abstract

This lab study was undertaken to analyze the effects of torque forces and shear modulus of rigidity on three circular solids namely, half-hard brass (60% Cu and 40% Zn), 0.1% and 0.4% carbon steel. This was done by subjecting the samples to a shearing stress and by noting down its angular displacement. The maximum torque of each sample was calculated and compared. Their polar moment of inertia was also calculated to assist in analysis. The value of shear modulus of rigidity of each of the samples was determined using a graph which related torque and angular displacement. It was ...

Abstract

The experiment involved the investigation of the young’s modulus of different beams made from different materials. The beams that were used for the test were steel, aluminum and timber. The experiment involved placing of the beams on the measurement machine shown below and addition of loads at the center of the beam. The loads were then varied across the beams while investigating the relationship that existed between the beams when different loads were added. The height, width, and the respective deflections were therefore recorded for analysis. The dial gauge was used to measure the deflection of the beam ...

DEFLECTION OF BEAMSIntroduction

Any kind of modern day construction makes use of a component called structural beam, or beam. A beam helps in adding strength of any design or structure. Generally manufactured using steel, wood, or concrete, it is commonly used for spanning any open element of a structure. In any design work based on iron, steel I beam is the most commonly used one. On the other hand, home-based constructions generally make use of wooden beams. When steel I beam is encased within concrete, it forms a concrete beam and is typically used in the construction of heavy structures, such as ...

Abstract

In this experiment, the young modulus of three beams was investigated these were steel, aluminum and timber. The beams were placed and the deflections values upon addition of various loads at the Centre of the beam taken. There was a variation of the loads across the beam to investigate thee relationship that existed between the loads, the span width, height, and deflections. Measurement of the deflection was therefore done through the dial gauge with three sets of measurements being taken and the average calculated. Different beams were used to enable elaborate comparison of the coefficient of elasticity. Measurement of ...

Abstract

The aim of this experiment was to determine the relationship between the Young’s Modulus and the deflection of a beam. Since different materials have different values of Young’s Modulus, the students selected three different materials for the experiment. In this case, the materials used include timber, aluminium, and steel. All the materials were identical in terms of the dimensions such as width and length. The each beam of the three materials was subjected to some magnitude of force at the centre and deflection measured. Data concerning the magnitude of load and the corresponding defection were then gathered ...

Introduction

Bend (flexure) testing is often done in springs as well in brittle materials whose behaviors of failure are linear like concrete, wood, plastic, glass and ceramics. Bend testing is suitable for evaluating the strength of brittle materials where the results of tensile tests aren’t easy to interpret due to the breaking of specimens around the gripping (Schoffstall, Charles, and Robert 234). In bend testing experiment, smooth rectangular specimens without notches are recommended under three or four point bend arrangements. Figure I below illustrates three point and four point bend arrangements respectively. Figure 1. Bend testing of a smooth ...

1- What are the differences between G’, G’’, and phase angle?

G’ is called the elastic modulus and it represents the energy that structured system will gain from the oscillatory motion as long as the motion is not disrupting the structure. It is also called the storage modulus as it describes the energy stored in the structure. If the interaction between the ingredients, are high then the value of G’ will also be high.

G” is called the viscous modulus also known as the loss modulus. This describes the part of energy that is lost as a result of the ...