Subject 2014 Question Paper — Government College of Engineering and T…

Instructions

• Attempt five questions in all selecting at least two questions from each Section.
• Assume missing data if any.
• All questions carry equal marks.

Questions

Section - A

• Q1. (a) Derive an expression for the elongation of a conical bar due to its self-weight. (b) Two prismatic bars are rigidly fastened together and support a vertical load of 40 KN as shown in figure 1. The upper bar is of steel having unit weight $760\text{ kN/m}^3$, length $10\text{ m}$ and cross sectional area of $80.7\text{ cm}^2$. The lower bar is of brass having unit weight $800\text{ kN/m}^3$, length $6\text{ m}$ and cross – sectional area $64.5\text{ cm}^2$. For steel $E = 207\text{ GPa}$ and brass $E = 90\text{ GPa}$. Determine: (i) Extension of free end due to self –weight only (ii) Maximum stress in each material. [20 marks]
• Q2. A simply supported beam with equal overhangs on either side as shown in Figure 2 carry UDL on entire length. If position of support is adjustable then draw SFD and BMD if: (i) $l > 2a$ (ii) $l = 2a$ (iii) $l < 2a$ Where a is overhand on each side. Also find position of supports when max. BM will be minimum possible and find the percentage overhand on each Side. [20 marks]
• Q3. Two rectangular plates, one of steel and the other of brass each $40\text{ mm}$ wide and $10\text{ mm}$ deep are placed together to form a beam $40\text{ mm} \times 20\text{ mm}$. Which is simply supported at ends and having span of $1000\text{ mm}$. The brass plate being on the top of the steel plate. Determine the maximum load which can be applied at the center of the beam, if the plates are: (i) put one over other (ii) firmly secured throughout their length Maximum allowable stress in steel is $112.5\text{ N/mm}^2$ and in brass is $75\text{ N/mm}^2$. Take $E_s = 200\text{ GPa}$ and $E_b = 80\text{ GPa}$. [20 marks]
• Q4. The composite beam shown in the Figure 3 is simply supported and carries a total uniform load of $50\text{ kN/m}$ on a span of $4.0\text{ m}$. The beam is built of a wood member having cross sectional dimensions $150\text{ mm} \times 250\text{ mm}$ and two steel plates of cross sectional dimensions $150\text{ mm} \times 50\text{ mm}$. Determine the maximum stresses in steel and wood respectively. If the moduli of elasticity are $E_s = 209\text{ GPa}$ and $E_w = 11\text{ GPa}$ (Disregard the weight of the beam). [20 marks]

Section - B

• Q5. A short C.I. column has a rectangular section $16\text{ cm} \times 20\text{ cm}$ with a circular hole of $8\text{ cm}$ diameter as shown in figure. It carries an eccentric load of 10 tonnes, located as shown in the figure 4. Determine the values of the stresses at the four corners of the Section. [20 marks]
• Q6. An over hand beam ABC is loaded as shown in figure 5. Determine slope and deflection of the beam at point C. Take $EI = 30\text{ MN-m}^2$. [20 marks]
• Q7. A solid shaft of $20\text{ cm}$ diameter has the same cross – sectional area as a hollow shaft of the same material with inside diameter of $15\text{ cm}$. (a) Find the ratio of horse powers transmitted by the two shafts at the same angular velocity. (b) Compare the angles of twist in equal lengths of these shafts, when stressed to the same intensity. [20 marks]
• Q8. A point in a strained material, is subjected to stresses as shown in figure 6. Find graphically the normal and tangential stresses across the plane EF. Check the answers analytically. [20 marks]