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Solution 827HideClick here to show or hide the solutionApply three-moment equation to first and middle spans

Where,

Thus,

equation (1)

Apply three-moment equation to middle and last spans

Where,

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Thus,

equation (2)

Solving equations (1) and (2) simultaneouslyanswer

answer

1 Pa = 1 N/m

1 kPa=

1 kN/m 1 MPa = 1 MN/m

= 1 N/mm

The meaning of kPand MPais very important because you'll need to understand the

concept of stress and strenght. Look for prefixes like kand Min the table above.

Formulae

However, the most common formulae are listed below:

Force = mass acceleration (F = m a)

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Weight = mass gravitational acceleration(W = m g)

Stresses (tension and compression) = force / area ( = F / A)

Density for major structural material

MaterialMass density

(kg/m3)

Weight density

(kN/m3)

Concrete(reinforced)

2500kg/m3 25kN/m

3

Concrete(unreinforced)

2300kg/m3 23kN/m

3

Brickwork 1900 kg/m 19kN/m

Timber(Softwood)

600 to 800kg/m3 6 to 8kN/m

3

Timber(Hardwood)

800 to 1100kg/m3 8 to 11kN/m

3

Steel 7850kg/m 78.5kN/m

By closely looking at the units we can easily work out the correct answer of a

propblem by substituting the units into the formula.

Consider the following example to work out the weight of a structural component or

member:

To calculate the weight of a component or member we use the formula:

Weight (W) = Density Volume

Remember unit for density is kg/m3and the unit for volume is m3but the unit for weight is measured in newton.

We need to convert the mass into a weight figure.

Weight = mass gravitational acceleration

W = m g(g = 9.81 m/s2but we use 10 m/s2)

Having converted the mass unit into a weight figure we can now calculate the weight

of any structural component or member in newtons by using:

W = kN/m3 m3

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