Note: Assume the suitable data if any.

$1.$ Determine the support reactions of the fixed beam shown in Figure $1.$ Neglect horizontal reactions.

OR

$(14$ Marks$)$

$(1)$ Determine the force in various members of the pin$-$jointed frame as shown in Figure $2.$ Take $\backslash (\backslash$mathrm$\{$AE$\}=15\backslash$times $10^\{5\}\backslash$mathrm$\{$kN$\}\backslash )$ for all members.

$(14$ Marks$)$

$2.$ A parabolic arch, hinged at the ends has a span $40$ m and rise $5$ m $.$ A concentrated load of $15$ KN acts at $10$ m from left hinge. The second moment of area varies as the secant of the slope of the rib axis.

$($a$)$ Calcuiate the horizontal thrust and the reactions at the hinges

$(6$ Marks$)$

$($b$)$ Calculate the maximum bending moment anywhere on the arch.

$(7$ Marks$)$

OR

$2.$ The cable $\backslash ($ A B $\backslash )$ shown in Figure. $3$ is subjected to a uniform loading of $\backslash (200\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ If the weight of the cable is neglected and the slope angles at points A and B are $\backslash (30^\{\backslash$circ$\}\backslash )$ and $\backslash (60^\{\backslash$circ$\}\backslash ),$ respectively,

$($a$)$ Determine the curve that defines the cable shape.

$($b$)$ Find the maximum tension developed in the cable.

$3.$ Draw $($approximately$)$ the moment diagram of the building frame shown in figure $4.$ Each column has the cross$-$sectional area indicated. Use the cantilever method OR the portal method. Note: Assume the data wherever required.

$1.$ Determine the support reactions of the fixed beam shown in Flgure $1$ using force method.

$(14$ Marks$)$

OR

$1.$ Determine the force in various members of the pin$-$jointed frame as shown in Figure $2$ using force method.

Take $\backslash ($ A E$=9\backslash$times $10^\{5\}\backslash$mathrm$\{$kN$\}\backslash )$ for all members.

$(14$ Marks$)$

FIG. $2$

$2.$ A parabolic arch, hinged at the ends has a span $30$ m and rise $5$ m $.$ A concentrated load of $12$ KN acts at $10$ m from left hinge. The second moment of area varies as the secant of the slope of the rib axis. $($Calculate the horizontal thrust and the reactions at the hinges. Also, calculate the $($maximum bending moment anywhere on the arch.

$2.$ Calculate the fixed end moments for the beam shown in Figure. $3$ using the column analogy method. Assume constant El$.$

$(13$ Marks$)$

The cable $\backslash ($ A B $\backslash )$ shown in Figure. $4$ is subjected to a uniform loading of $\backslash (200\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ If the weight of the cable is neglected and the slope angles at points $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are $\backslash (30^\{\backslash$circ$\}\backslash )$ and $\backslash (60^\{\backslash$circ$\}\backslash ),$ respectively, determine the curve that defines the cable shape and the maximum tension developed in the cable.

OR inclined at an angle $\text{'}\backslash (\backslash$beta $\backslash )\text{'}$ to the vertical as shown in Figure$\mathrm{.}5.$ Locate the neutral axis if $\backslash (\backslash$beta$=2^\{\backslash$circ$\}\backslash )$ and find the flexural stress at the corner $\text{'}\backslash ($ C$^\{\backslash$prime$\}\backslash )\text{'}$ in terms of $\backslash ($ M $\backslash ).$ Find out the factor by which this stress is increased by changing $\text{'}\backslash (\backslash$beta$^\{\backslash$prime$\}\backslash )$ from $\backslash (0^\{\backslash$circ$\}\backslash )$ to $\backslash (2^\{\backslash$circ$\}\backslash ).$