Question Two

A rigid bar ACB is supported on a fulcrum at $C$ and loaded by a force $P$ at end $B.$ Three identical wires made of an elastoplastic material $($yield stress ${}_Y$ and modulus of elasticity $E)$ resist the load $P.$ Each wire has cross$-$sectional area A and length $L.$

a$)$ Determine the yield load $P_Y$ and the corresponding yield displacement $d_Y$ at point $B.$

b$)$ Determine the plastic load $P_P$ and the corresponding displacement $d_P$ at point $B$ when the load just reaches the value $P_P.$

c$)$ Draw a load$-$displacement diagram.

Answer

a$)P_Y={}_{Y}A,d_Y=1\mathrm{.}5{}_Y\frac{L}{E}$

b$)P_P=3{}_{Y}A,d_Y=3{}_Y\frac{L}{E}$

Vraag Twee

$\text{'}$n Starre staaf ACB word ondersteun op $\text{'}$n draaipunt by $C$ en gelaai deur $\text{'}n$ krag $P$ aan die einde $B.$ Drie identiese drade gemaak van $\text{'}n$ elastoplastiese materiaal $($vloeispanning ${}_Y$ en elastisiteitsmodulus $E)$ weerstaan die las $P.$ Elke draad het $\text{'}n$ dwarssnee$-$area $A$ en lengte $L.$

a$)$ Bepaal die vloeilading $P_Y$ en die ooreenstemmende vloei$-$verplasing $d_Y$ by punt $B.$

b$)$ Bepaal die plastiese las $P$ en die ooreenstemmende verplasing $d_P$ by punt $B$ wanneer die las net die waarde $P_P$ bereik.

c$)$ Teken $\text{'}$n las$-$verplasing diagram.

Antwoord

a$)P_Y={}_{Y}A,d_Y=1\mathrm{.}5{}_Y\frac{L}{E}$

b$)P_P=3{}_{Y}A,d_Y=3{}_Y\frac{L}{E}$

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Departement Siviele Ingenieurswese $/$ Department of Civil Engineering

Sterkteleer $254/$ Strength of Materals