written 6.4 years ago by | modified 5.4 years ago by |
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.
written 6.4 years ago by | modified 5.4 years ago by |
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.
written 6.4 years ago by | • modified 6.4 years ago |
Note: Myy B.M coming negative as 80kN(D) and 600kN(A) taking as compression side but it results in tension
written 5.4 years ago by | • modified 5.4 years ago |
[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]