Step 1: Understanding Limit State Design (LSD).
In limit state design, partial safety factors are applied to material strengths to account for variability, uncertainties, and ensure safety.
Step 2: IS 456:2000 provisions.
According to IS 456:2000, the recommended partial safety factors are:
- For concrete: \(\gamma_{m} = 1.5\)
- For steel: \(\gamma_{m} = 1.15\)
Step 3: Why not other options?
- (B) 1.67 and 1.5: These were used in working stress method, not LSD.
- (C) 3 and 1.5: Not relevant to RCC design.
- (D) 1.5 and 1.2: Incorrect values for LSD.
Step 4: Conclusion.
Thus, the partial safety factors for concrete and steel are \(\,1.5 \,\text{and}\, 1.15\).
The solution(s) of the ordinary differential equation $y'' + y = 0$, is:
(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:
For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is: