Recent questions tagged numerical-answers

A steel strip of length $L=200$ mm is fixed at end $A$ and rests at $B$ on a vertical spring of stiffness, $k=2 \: N/mm$. The steel strip is $5$ mm wide and $10$ mm thick...

According to the concept of Limit State Design as per $IS \: 456:2000$, the probability of failure of a structure is ______.

A $588 \: cm^3$ volume of moist sand weighs $1010$ gm. Its dry weight is $918$ gm and specific gravity of solids, $G$ is $2.67$. Assuming density of water as $1 \: gm/cm^...

A $4$ m thick layer of normally consolidated clay has an average void ratio of $1.30$. Its compression index is $0.6$ and coefficient of consolidation is $1 \: m^2/yr$. I...

A pile of diameter $0.4$ m is fully embedded in a clay stratum having $5$ layers, each $5$ m thick as shown in the figure below. Assume a constant unit weight of soil as ...

A field channel has cultivable commanded are of $2000$ hectares. The intensities of irrigation for gram and wheat are $30 \%$ and $50\%$ respectively. Gram has a kor peri...

A triangular gate with a base width of $2$ m and a height of $1.5$ m lies in a vertical plane. The top vertex of the gate is $1.5$ m below the surface of a tank which con...

A pipe of $0.7$ m diameter has a length of $6$ km and connects two reservoirs A and B. The water level in reservoir A is at an elevation $30$ m above the water level in r...

A landfill is to be designed to serve a population of $200000$ for a period of $25$ years. The solid waste (SW) generation is $2$ kg/person/day. The density of the un-com...

A water treatment plant of capacity, $1 \: m^3/s$ has filter boxed of dimensions $6 \; m \times 10 \: m$. Loading rate to the filters is $120 \: m^3/day/m^2$. When two of...

In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of $32.5 \: m^3/day/m^2$ is $32.5$ m long, $8.0$ m wide and liquid depth of...

The relation between speed $u$ (in km/h) and density $k$ (number of vehicles/km) for a traffic stream on a road is $u=70-0.7k$. The capacity on this road is _________ vph...

Two Pegs A and B were fixed on opposite banks of a $50$ m wide river. The level was set up at A and the staff readings on Pegs A and B were observed as $1.350$ m and $1.5...

The exports and imports (in crores of Rs.) of a country from the year $2000$ to $2007$ are given in the following bar chart. In which year is the combined percentage incr...

For what value of $p$ the following set of equations will have no solution?$2x+3y=5$$3x+py=10$

Consider the following probability mass function (p.m.f) of a random variable $X:$$$p(x,q) = \begin{cases} q & \text{ if } X=0 \\ 1 – q & \text{ if } X=1 \\ 0 & \text{oth...

The development length of a deformed reinforcement bar can be expressed as $(1/k) (\phi \sigma_s / \tau_{bd})$. From the $IS: 456 – 2000$, the value of $k$ can be calcula...

For the beam shown below, the value of the support moment $M$ is _____ $kN-m$.

Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, $\sigma_n$ is _______ MPa.

The penetration value of a bitumen sample tested at $25^{\circ}C$ is $80$. When this sample is heated to $60^{\circ}C$ and tested again, the needle of the penetration tes...

The quadratic equation $x^2 – 4x +4 =0$ is to be solved numerically, starting with the initial guess $x_0=3$. The Newton-Raphson method is applied once to get a new estim...

The directional derivative of the field $u(x,y,z) = x^2-3yz$ in the direction of the vector $(\hat{i}+\hat{j}-2 \hat{k})$ at point $(2, -1, 4)$ is _________.

The composition of an air-entrained concrete is given below:$\begin{array}{lcr} \text{Water} & : & 184 \: kg/m^3 \\ \text{Ordinary Portland Cement (OPC)} & : & 368 \: kg/...

The bracket plate connected to a column flange transmits a load of $100$ kN as shown in the following figure. The maximum force for which the bolts should be designed is ...

Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section from $IS:456-2000$ are also given below (right fi...

For formation of $\textit{collapse mechanism}$ in the following figure, the minimum value of $P_u$ is $cM_p/L$. $M_p$ and $3M_p$ denote the plastic moment capacities of b...

A tapered circular rod of diameter varying from $20$ mm to $10$ mm is connected to another uniform circular rod of diameter $10$ mm as shown in the following figure. Both...

Two beams are connected by a linear spring as shown in the following figure. For a load $P$ as shown in the figure, the percentage of the applied load $P$ carried by the ...

For the $2D$ truss with the applied loads shown below, the strain energy in the member $XY$ is _____ kN-m. For member $XY$, assume $AE=30$ kN, where $A$ is cross-section ...

A water tank is to be constructed on the soil deposit shown in the figure below. A circular footing of diameter $3$ m and depth of embedment $1$ m has been designed to su...

A $20$ m thick clay layer is sandwiched between a silty sand layer and a gravelly sand layer. The layer experiences $30$ mm settlement in $2$ years.Given:$T_v = \begin{ca...

A non-homogeneous soil deposit consists of a silt layer sandwiched between a fine-sand layer at top and a clay layer below. Permeability of the silt layer is $10$ times t...

A square footing $(2\:m \times 2\:m)$ is subjected to an inclined point load, $P$ as shown in the figure below. The water table is located well below the base of the foot...

A hydraulic jump is formed in a $2$ m wide rectangular channel which is horizontal and frictionless. The post-jump depth and velocity are $0.8$ , and $1$ m/s, respectivel...

A short reach of a $2$ m wide rectangular open channel has its bed level rising in the direction of flow at a slope of $1$ in $10000$. It carries a discharge of $4 m^3/s$...

The concentration of Sulfur Dioxide $(SO_2)$ in ambient atmosphere was measured as $30 \: \mu g /m^3$. Under the same conditions, the above $SO_2$ concentration expressed...

Consider a primary sedimentation tank (PST) in a water treatment plant with Surface Overflow Rate (SOR) of $40\:m^3/m^2/d$. The diameter of the spherical particle which w...

A sign is required to be put up asking drivers to slow down to $30$ km/h before entering Zone $Y$ (see figure). On this road, vehicles require $174$ m to slow down to $30...