Ouestion $No,31(40)$

Figure $3$ shows the roof layyout of a building. All structural elements are cast in place. It is required to:

a$-$ Draw the bending moment diagram of the beam on Axis $($B$)$ using the given losade.

b$-$ What is the type of the section at midspan?

$($i$.$e$.$ Rectangulur, T$,$ or doubly reinforced section$)$

Ans

b$-$ Design the critical section at the mid$-$span of the beam on Axis $($B$).$ The spacing between beams is $3\mathrm{.}0m$ and its span is $12\mathrm{.}0m.$

c$-$ Draw the cross$-$section of the beam showing reinforcement details.

Given Data:

Given loads are unfactored loads $)$ and include :

${}_c=25k\frac{N}{m^3}$

$f_c=28$MPa,$f_y=420$MPa,

Use bar size # $16$

Depth, $d=620mm$ should be used in the design

Design Aids:

$\backslash$table$[[$Minimum slab$/$beam height $($thickness$)$ h$],[,$Simply supported,One end continuous,Both end continuous,Cantilever$],[$Solid one way slabs,L$/20,$L$/24,$L$28,$L$10],[$Beams or ribbed one$-$way slabs,L$/16,$L$18\mathrm{.}5,$L$/21,$L$8]]$

Where $L$ is the beam span

Calculations of Bending Moments

For simple beams:

Uniform load: B$.$M$.=wu\frac{I^2}{8}$

Concentrated load at the middle: B$.$M$.=P{u}_{u}14$

For Cantilever:

Uniform load: B$.$M$.=W\frac{u^2}{2}$

Concentrated load at the cantilever tip: B$.$M$.=Pu$