# Daily Archives: March 9, 2021

## Design a rectangular pre-stressed beam section (on allowable stress basis) that supports a live load of 2.5 k/ft on a span of 30 ft. Pre-stress losses = 22%. fc 6000 psi, ftt = -208 psi, fct = 2880 psi, fcs = 3600 psi, fts = -465 psi.

1.A rectangular beam of 12 in. width and 18 in. depth is pre-stressed by a force of 20 kip applied through a tendon of wires of 2 in. diameter located 3 in. from the bottom. The beam carries a load of 2 k/ft over a span of 20 ft. The pre-stress losses are 25%. Compute the stresses in concrete at the (1) transfer stage, and (2) service load stage. The density of concrete is 145 lbs/ft3. 2. The compressive strength of concrete is 5000 psi. Accordingly, the allowable stresses are the following: ftt = the allowable tensile stress in concrete at initial transfer of pre-stress = -190 psi fct = the allowable compression stress in concrete at initial transfer of pre-stress = 2400 psi fcs = the allowable….

## Determine the maximum unbraced length of beam to satisfy the requirement of adequate lateral support.

1. For the braced column section and the loading shown in Figure P10.20, determine the limit states for which the column should be designed. Use A992 steel 2. Design a beam of A36 steel for the loads in Figure P11.1. Determine the maximum unbraced length of beam to satisfy the requirement of adequate lateral support. 3. Design a simply supported 20 ft span beam of A992 steel having the following concentrated loads at the midspan. Service dead load = 10 k Service live load = 25 k Determine the maximum unbraced length of beam to satisfy the requirement of adequate lateral support.

## Design a beam of A992 steel for the loading shown in Figure P11.2.

1.Design a beam of A992 steel for the loading shown in Figure P11.2. The compression flange bracing is provided at each concentrated load. The selected section should be such that the full lateral support condition is satisfied. Determine the maximum unbraced length of beam to satisfy the requirement of adequate lateral support. 2. Design a cantilever beam of A992 steel for the loading shown in Figure P11.3. The compression flange bracing is provided at each concentrated load. The selected section should be such that the full lateral support condition is satisfied. Determine the maximum unbraced length of beam to satisfy the requirement of adequate lateral support.

## How much fees could HFRI replication charge before falling below S&P Sharpe ratio?

1. How has DELTA done vs. HFRI_FW and S&P index? Compute the mean return,

volatility, Sharpe ratio, and correlations of DELTA with the indices, for the whole period

as well as two subperiods (2008-2009 and 2010-2011). What is the simple cumulative

return for DELTA and HFRI_FW and S&P index in the whole period from 2008 Oct to

2011 May? If you start with 1\$ in each of these in beginning of Oct 2008, how much

money you will end up with in 2011 May?

2. Using a four-factor model that is expanded from Fama-French three-factor model by

adding a Momentum factor, please evaluate the performance of HFRI equity hedge total

return index and the DELTA strategy. Interpret your regression results. Do they

outperform? What are their exposures….

## Calculate the maximum achievable bridge out-of-balance voltage for an applied torque T of 103 N m given the following

Four strain gauges, with specification given below, are available to measure the torque on a cylindrical shaft 4 cm in diameter connecting a motor and load.

(a) Draw clearly labelled diagrams showing:

(i) the arrangement of the gauges on the shaft;

(ii) the arrangement of the gauges in the bridge circuit, for optimum accuracy and sensitivity.

(b) Calculate the maximum achievable bridge out-of-balance voltage for an applied torque T of 103 N m given the following:

Tensile and compressive strains  is the shear modulus of the shaft material and a is the radius of the shaft in metres.

## Find the gain and phase characteristics of the maintaining amplifier.

A solid-state capacitive humidity sensor has a capacitance given by:

C = 1.7 RH + 365pF

where RH is the percentage relative humidity. The sensor has an associated parallel resistance of 100 kΩ. The sensor is incorporated into a feedback oscillator system with a pure inductance and a maintaining amplifier. The oscillator is to give a sinusoidal output voltage at the natural frequency of the L–C circuit for a relative humidity between 5 and 100%.

(a) Draw a diagram of a suitable oscillator system.

(b) If the frequency of the output signal is to be 100 kHz at RH = 100%, calculate the required inductance.

(c) Find the gain and phase characteristics of the maintaining amplifier.

## calculate the mean velocity of the gas at maximum flow rate

A pitot tube is used to measure the mean velocity of high pressure gas in a 0.15 m diameter pipe. At maximum flow rate the mean pitot differential pressure is 250 Pa. Use the data given below to:

(a) calculate the mean velocity of the gas at maximum flow rate;

(b) estimate the maximum mass flow rate;

(c) estimate the Reynolds number at maximum flow;

(d) explain why an orifice plate would be suitable to measure the mass flow rate of the gas. (e) Given that a differential pressure transmitter of range 0 to 3 × 104 Pa is available, estimate the required diameter of the orifice plate hole (assume coefficient of discharge = 0.6, expansibility factor and velocity of approach factor = 1.0).

## Calculate an accurate value for the differential pressure developed across the chosen Venturi, at maximum flow rate.

A Venturi is to be used to measure the flow rate of water in a pipe of diameter D = 0.20 m. The maximum flow rate of water is 1.5 × 103 m3 h−1, density is 103 kg m−3, and viscosity is 10−3 Pa s. Venturis with throat diameters of 0.10 m, 0.14 m and 0.18 m are available from the manufacturer.

(a) Choose the most suitable Venturi for the application, assuming a differential pressure at maximum flow of approximately 3 × 105 Pa.

(b) Calculate an accurate value for the differential pressure developed across the chosen Venturi, at maximum flow rate. (Use the following formula for the coefficient of discharge:

where

d = Venturi throat diameter, and ReD = Reynolds number referred to pipe diameter.)

## sketch the form of the output signal when T = 2000 K.

A thermocouple has an e.m.f. of 5 mV when the hot junction is at 100 °C and the cold junction is at 0 °C. A thermopile consisting of 25 such thermocouples in series is used as a detector in a chopped, broadband pyrometer. When unchopped the power in the beam of radiation incident on the hot junction of the thermopile is given by 7.5T 4 pW, where T K is the temperature of the distant target. The beam is chopped by a semicircular disc rotating at 6000 r.p.m. The reference junction of the thermopile is at the temperature of the pyrometer

enclosure. Assuming the thermocouples are linear and the detector data given below, sketch the form of the output signal when T = 2000 K.

## calculate the power incident on the detector and the detector output current.

An optical fibre transmission system consists of a circular LED source, a 2-metre length of optical fibre and a circular PIN diode detector. Both the source and detector are positioned 100 µm from the ends of the fibre. Detailed data for the source, a glass fibre, a polymer fibre and the detector are given below. Use this data to perform the following calculations.

(a) The total power Ps emitted by the source in all directions (use eqn [15.23b]).

(b) The numerical aperture and maximum angle of acceptance of the glass fibre.

(c) The numerical aperture and maximum angle of acceptance of the polymer fibre.

(d) The source and detector are linked by the glass fibre; calculate the power input to the fibre, the fibre transmission factor, and power….