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An R.C.C footing is having dimension as shown in fig. It carries 4 load as indicated. Calculate the resultant stress at corners A,B,C,D.

An R.C.C footing is having dimension as shown in fig. It carries 4 load as indicated. Calculate the resultant stress at corners A,B,C,D. 1

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1 2 Note: Myy B.M coming negative as 80kN(D) and 600kN(A) taking as compression side but it results in tension 3

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[1] Area of footing = (2+2)×(1+1)=8m2

Section modulus about XX – axis = bd312(d2)=bd26

(Z=IY)

=4×226=2.67 m3

Section modulus about YY – axis = db36=2×436

= 21.33 m3

[2] Direct stress due to direct load

Pd=Total LoadArea=600+500+700+8008

=325 KN/m2 - - -[C]

[3] B.M due to load eccentric about the axis XX:

Mxx=[800×0.6+700×0.8][600×0.4+500×0.5]

Max stress due to above B.M = \pm \frac{Mxx}{Zxx}

= \frac{550}{2.67} = \pm 206 \ KN/m^2

(Compress at C and D, tensile at A & B).

B.M due to eccentric about the axis YY.

M_{yy} = (600 \times 0.9 + 800 \times 0.6) – (500 \times 0.8 + 700 \times 1.5)

= -430 KNm.

\therefore Max stress due to above B.M = \frac{+M_{yy}}{Z_{yy}} = \pm \frac{430} {21.33}

= \pm 20.15 \ KN/m^2

(Compressive at B, C & tensile at A & D).

Note: Myy B.M coming negative as 80kN(D) and 600kN(A) taking as compression side but it results in tension

Hence resultant stress at corners of footing:

Stress at A = 325 – 206 – 20.15 = 98.85 [C]

Stress at B = 325 – 206 + 20.15 = 139.15 [C]

Stress at C = 325 = 206 + 20.15 = 551.15 [C]

Stress at D = 325 + 206 – 20.15 = 510.85 [C]

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