. Assume a continuous function f(x) defined on x axis with a uniform grid spacing of h. The first and second derivatives of function can be approximated using information at more grid points giving rise to higher-order approximations. Using appropriate Taylor series expansions about location x, find the leading order truncation terms for the following approximations. Also indicate the order of accuracy for each approximation. Show all steps and box the final answers. Note: Look for the location at which a particular formula is written. For example, the first one below is at the location x. All your Taylor series expansions should be around x in this case. If a formula is approximating at x + h, all your Taylor series expansions should be around x + h (e.g. for part 4).

f(x + h) ≈ 2f(x) − f(x − h)

An arch dam has the following characteristics.

H= 22.2 m, L1=400m, L2=120 m, Find the thickness and projection on the crown cantilever and volume of the concrete.

Renaissance, in the sense of rebirth, occurs often in history. What was so special about the Fifteenth and Sixteenth century Renaissance to set it apart from all others so that the time period carries this title?

Five paragraph essay

On a daily basis, researchers challenge and improve existing concrete strength and properties. Discuss the latest achievements in the concrete strength domain. Also, compare recent United States research accomplishments in that field with those of the rest of the world.

Is BIM a new technology, or a new process, or both? What are the promises that BIM holds to the industry? How does BIM impact the construction industry? Discuss the factors that affect the business value of BIM. Discuss the reasons that some companies still would not use BIM.

How does society resolve the debate that arises from the conflict between groups advocating building vs. removing infrastructure in the names of human needs vs. environmental needs? What role do environmental engineers play in resolving the debate?

Using the following data for an unreinforced PCC Pavement slab: ■ Design strength f′ c = 28 MPa ■ Slab thickness = 300 mm ■ Standard deviation of f′ c obtained from 20 samples = 1.4 MPa ■ Ignore any exposure requirement ■ Use air-entrained concrete ■ Fineness modulus of fine aggregate = 2.60 ■ Maximum aggregate size = 50 mm and nominal maximum aggregate size = 37.5 mm ■ Bulk oven-dry specific gravity of coarse aggregate = 2.6 ■ Oven-dry rodded density of coarse aggregate = 2002 kg/m3 Find the following: a. Required compressive strength b. w/c ratio c. Coarse aggregate amount (kg/m3 ) d. If the w/c ratio is 10% reduced, will the quantity of coarse aggregate increase, decrease or remain the same? Explain your answer.

the fourth treatment stage know as aquifer recharge, involves either holding the water at a pool from which it seeps into the underlying aquifer, or directly injecting the water into the subsurface. which of the two methods can improve the quality of water, explain in short

To what temperature (in °C) must a cylindrical rod of one metal 10.045 mm in diameter and a plate of second metal having a circular hole 9.990 mm in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is 25°C and that the linear expansion coefficient values for metals one and two are 4.9 x 10^-6 (°C)^-1 and 17 x 10^-6 (°C)^-1, respectively.

There are several steps in a basic level-of-service determination for an uninterrupted flow facility. Briefly define the following three facilities: 1) basic freeway 2) multilane highway and 3) two-lane highway. Furthermore, compile a table with the base conditions and steps (formulas/equations/tables) on how to determine the level of service of each of the three facilities listed above.

Design a plain concrete mix required for 400mm deep RCC beam to be constructed in New Girls Hostel at GIK Institute (you can assume workability). The specified compressive strength is 32 MPa at 28 days. The standard deviation of the concrete producer is 3.0 MPa. Select nominal maximum-size coarse aggregate from following data

1. Min. distance b/w two reinforcing bar is 40mm
2. Min. distance b/w reinforcing bar and concrete surface (clear cover) is 42mm
3. Thick of slab is 120mm
4. Concrete is not pump-able

The specific gravity of fine aggregate (FA) and coarse aggregate (C.A) are 2.5 and 2.6 respectively. The dry rodded bulk density of C.A. is 1650 kg/m3, and fineness modulus (FM) of FA is 2.70.

C.A. is found to be absorptive to the extent of 5 % and free surface moisture (moisture content) in sand is found to be 5 per cent .Assume any other essential data, concrete should be durable against sulfate and chloride attack.

Question 5 (1 point)

Match the term with the definition.

Question 5 options:

A singly reinforced beam 47.2cm×28.3cm, is provided with 5 bar of each diameter 2.2cm. determine:
1) percentage of excess steel used
2) moment of resistance
3)Actual stress develop in steel and concrete
4) maximum allowable central load that can be put if it is carrying a uniformly distributed load of 850kg/m over a simple supported length of 3.2m.

(note : we have exam right now please help please ???)

How the behavior of a SDOF is going to be affected by a non-linear elastoplastic behavior of the spring? Why?