QUESTION ONE $(50)$

Briefly define the following terms: $(10)$

a$)$ Ductility $($give one example for the material that behaves in this manner$)$

b$)$ Fracture $($give one example for the material that behaves in this manner$)$

c$)$ Shape factor

d$)$ Determinate

e$)$ Indeterminate

f$)$ Figure Q$1($a$)$ shows a prismatic beam loaded with a uniformly distributed dead load of $20$

$k\frac{N}{m}$ and a concentrated load of $100kN.$ The beam is made of material whose young

modulus of elasticity is $210$GPa and of cross$-$section shown in Figure Q$1($b$).$ Use the

beam and the cross section below to answer the following questions.

g$.$ Use the equilibrium equation and equation of conditions to determine the reactions at the

supports.

h$.$ Draw the shear force and bending moment diagrams indicating all the key values.

i$.$ Draw the qualitative shape of the beam.

j$.$ Determine the shear stress at all points where the stress changes at a cross section of a

beam where the shear force is maximum.

k$.$ Draw a diagrammatic sketch to show the shear stress distribution across the cross section.

Determine the maximum flexural stress in the beam. f$)$ Figure Q$1($a$)$ shows a prismatic beam loaded with a uniformly distributed dead load of $20$

$k\frac{N}{m}$ and a concentrated load of $100kN.$ The beam is made of material whose young

modulus of elasticity is $210$GPa and of cross$-$section shown in Figure Q$1($b$).$ Use the

beam and the cross section below to answer the following questions.

$I=413mm$

$f=180mm$

$f=16mm$

$N=9\mathrm{.}5$mmcalculation of a shape factor with a concrete block