Numerical Analysis

Assignment $5(80$ pts$)$

Problem Set I: Due $09$:$50$ AM$,$ May $24($Fri$)$

Problem Set II: Due $09$:$50$ AM$,$ May $31($Fri$)$

Problem Set I: Problems $1-10$

Fig. $1$ shows a reinforced concrete beam under a concentrated load,

$P=200kN$ at midspan.

Fig. $1$ Reinforced concrete beam under a concentric load at midspan

For this beam, the distribution of curvature $\frac{d^{2}y}{d{x}^2}=-(x)$ is given by:

$(x)=\frac{M(x)}{E_c*I_e(x)}$

where,

$I_e(x)=\frac{1}{\sqrt[\phantom{2}]{1+4*(\frac{x}{8}{)}^2}}$

$b,h$ and $L=350$

$I_o=\frac{b{h}^3}{12}$; and

$E_c=2{10}^4$MPa.

Problems $1$ and $2$: Mathematical expressions and plot

$(10$ pts$)$ Find mathematical expressions of $M(x)$ in $kN*m$ and $(x)$ in

$\frac{1}{m}.$

$(10$ pts$)$ Plot $M(x)$ and $(x),$ separately for the whole span.

Problems $3-5$: Hand calculations