The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 150-mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA 5 340 N ? m. The shaft is machined from steel with Sy 5 420 MPa and Sut 5 560 MPa. Using a factor of safety of 2.5, determine the minimum allowable diameter of the 250-mm section of the shaft based on (a) a static yield analysis using the distortion energy theory and (b) a fatigue-failure analysis. Assume sharp fillet radii at the bearing shoulders for estimating stress-concentration factors

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The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 150-mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA 5 340 N ? m. The shaft is machined from steel with Sy 5 420 MPa and Sut 5 560 MPa. Using a factor of safety of 2.5, determine the minimum allowable diameter of the 250-mm section of the shaft based on (a) a static yield analysis using the distortion energy theory and (b) a fatigue-failure analysis. Assume sharp fillet radii at the bearing shoulders for estimating stress-concentration factors

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(1) The Saudi Aluminum Company manufactures chair frames and television antennas. The production of an antenna requires 0.5 hours in the tube bending machine and 1 hour in the punching machine, while a chair frame requires 0.5 hours in each machine. The company has 4 hours available daily for the tube bending machine and 6 hours for the punching machine. If the net profit is 36 SAR per antenna and 24 SAR per chair frame, how many antennas and chair frames should the company produce daily to maximize profit?

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Al-Amal Marketing Center wants to advertise to its customers about the availability of hot drinks and light snacks in all its branches. The goal is to reach at least 60,000 men and 40,000 women in Jeddah using newspapers and local radio. It is expected that an advertisement in the newspaper will reach 6,000 men and 2,000 women, while an advertisement on the radio will reach 2,000 men and 4,000 women. The cost of a newspaper advertisement is 450 SAR per instance, and a radio advertisement costs 260 SAR per instance. Objective: Calculate the minimum-cost advertising strategy to reach the target audience. Decision Variables: Let: X1 = Number of newspaper advertisements X2 = Number of radio advertisements

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يريد مركز األمل للتسويق اإلعالن لزبائنه عن توفر المشروبات الســاخنــة والمأكوتت الخفيفة في جميع فروعه، ويريد أن يصـل اإلعالن إلى 60 ألف رجل و 40 ألف امرأه على األ ل في محافظة جدة مستخدما في ذلك الصحف واإلذاعة المحلية ، و ــــد تو ع أن يصل اإلعالن في الصحيفة إلى 6 آتف رجل و ألفين امرأة وأن يصـــــــــل اإلعالن في اإلذاعة إلى ألفين رجل و 4 آتف امرأة. وتبلغ تكلفة اإلعالن في الصحيفة 450 لاير للمرة الواحدة وفي اإلذاعة 260 لاير . أحســـز عـــدد اإلعالنات المطلوز إجرائها بأ ل تكلفة ممكنــــة لكي تصل اإلعالنات إلى العدد المطلوز الوصول إليه.، ضع المسألة السابقة في الصورة العامة للبرمجة الخطية؟ أفتر أن ?𝒙? = عـدد اإلعالنات في الصحيفة ?𝒙? = عـدد اإلعالنات في اإلذاعة وتصـبد دالة الهـدف 𝑴𝒊𝒏 𝒁 = 𝟒𝟓𝟎 𝒙𝟏 + 𝟐𝟔𝟎 𝒙𝟐 𝑺𝒖𝒃𝒋𝒆𝒄𝒕 𝒕𝒐 𝟔 𝒙𝟏 + 𝟐 𝒙𝟐 ≤ 𝟔𝟎 𝟐 𝒙𝟏 + 𝟒 𝒙𝟐 ≤ 𝟒𝟎 𝒙𝟏, 𝒙𝟐 ≥ ?

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c) A direct voltage of 50 volts and a direct current of 40 A are to be drawn from a single-phase half wave rectifier. The rectifier is connected to 220 v ac supply via a transformer. Calculate the values of the secondary a.c voltage, the secondary a.c current, the peak reverse voltage, the transformer apparent power, the transformer utilization factor, and the transformer turns ratio. d) Using the values obtained in (c) for the transformer, if a coil of 10 mH in connected in series with the resistor, draw the waveforms of the output voltage and current then calculate their values. e) If a freewheeling diode is connected in parallel with the load, draw the waveforms of the output voltage and current then calculate their values.

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Problem (1) a) What is the function of the capacitor placed at the output terminals of a rectifying circuit? b) Sketch the output voltage of a single-phase full wave bridge rectifier with and without the smoothing capacitor showing the effect on the ripple voltage. c) A direct voltage of 50 volts and a direct current of 40 A are to be drawn from a single-phase half wave rectifier. The rectifier is connected to 220 v a.c supply via a transformer. Calculate the values of the secondary a.c voltage, the secondary a.c current, the peak reverse voltage, the transformer apparent power, the transformer utilization factor, and the transformer turns ratio. d) Using the values obtained in (c) for the transformer, if a coil of 10 mH in connected in series with the resistor, draw the waveforms of the output voltage and current then calculate their values. e) If a freewheeling diode is connected in parallel with the load, draw the waveforms of the output voltage and current then calculate their values.

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Problem (2) a) What are the basis applied for selecting rectifier diodes.? b) A direct voltage of 30 volts and a direct current of 200 A are needed for a heater. A three-phase supply with 380 v is available. i. Sketch the input a.c voltage, output d.c voltage and current, diode currents, supply currents, and the diode voltage for; – A three-phase full wave rectifier. – A three-phase half-wave rectifier. ii. Calculate the values of the transformer secondary a.c voltage and a.c current, the peak reverse voltage, the transformer apparent power, the transformer utilization factor, and the transformer turns ratio for both configurations.

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