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Fatigue strength

In materials science, fatigue is the weakening of a material caused by repeatedly applied loads. Fatigue strength is a measure of the strength of a ... more

Creep (deformation)

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of ... more

Miles Equation

In 1954, Miles developed his version of this equation for GRMS as he was researching fatigue failure of aircraft structural ... more

Griffith's criterion in Linear elastic fracture mechanics (stress intensity factor)

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid ... more

Critical Buckling Stress of a Column with Buckling Coefficient

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Mohr–Coulomb failure criterion

Mohr–Coulomb theory is a mathematical model describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as ... more

AC Power

In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy ... more

Buckling Coefficient

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Critical buckling stress of a column

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Petroff's Law - shear stress in the lubricant

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

Apparent power

The power factor of an AC electrical power system is defined as the ratio of the real power flowing to the load, to the apparent power in the circuit. In a ... more

Rankine Gordon formula (Maximum axial load that a column will buckle)

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Bearing capacity for square foundations (Terzaghi's Theory)

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Bearing capacity for circular foundations (Terzaghi's Theory)

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Bearing capacity for continuous foundations (Terzaghi's Theory)

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Laser rangefinder - distance realtive to wavelength and number of cycle

A laser rangefinder is a rangefinder that uses a laser beam to determine the distance to an object. The most common form of laser rangefinder operates on ... more

Beale number

In mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power ... more

Cylindrical shells:ASME Boiler and Pressure Vessel Code (BPVC) (UG-27)

he ASME Boiler and Pressure Vessel Code (BPVC) is an American Society of Mechanical Engineers (... more

Anelastic Attenuation Factor

In reflection seismology, the anelastic attenuation factor, often expressed as seismic quality factor or Q (which is inversely proportional to attenuation ... more

West number

The West number is an empirical parameter used to characterize the performance of Stirling engines and other Stirling systems. A Stirling engine is a heat ... more

Stress-Optic Law

Photoelasticity is an experimental method to determine the stress distribution in a material.Unlike the analytical methods of stress determination, ... more

Properties of concrete - modulus of elasticity for normal weight concrete

The modulus of elasticity of concrete is a function of the modulus of elasticity of the aggregates and the cement matrix and their relative proportions. ... more

Spherical shells: ASME Boiler and Pressure Vessel Code (BPVC) (UG-27)

The ASME Boiler and Pressure Vessel Code (BPVC) is an American Society of Mechanical Engineers (... more

Maximum axial load that a long, slender, ideal column can carry without buckling

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Properties of concrete - modulus of elasticity

Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost ... more

Self-buckling critical height ( for a free-standing, vertical column)

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Mass of pressure Cylindrical vessel with semi-elliptical ends

Pressure vessels are held together against the gas pressure due to tensile forces within the walls of the container. The normal (tensile) stress in the ... more

Root mean square of phase-to-phase voltage

In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. In a balanced ... more

Properties of concrete - modulus of elasticity (AASHTO)

The modulus of elasticity of concrete is a function of the modulus of elasticity of the aggregates and the cement matrix and their relative proportions. ... more

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