AB and BC are spans of a fully continuous beam. AB is 10m. long carries a concentrated load of 10kN. applied 5m. from B, BC is 15m. long and carries a concentrated load of 20kN applied 9m. from B. If MA = – 20kN.m and MC = – 25kN.m, find the moment at B.
Solution:
A reinforce concrete spiral column having a diameter of 500mm carries an ultimate load Pu = 5,000 kN. If fc’ = 25MPa fy = 400MPa, find the number of 28mmθ bars. Use θ = 0.75.
Solution:
In design of reinforced concrete braced column members, the factor relating the actual moment diagram due to end moment M1 and M2 only (M1 ≤ M2) to an equivalent uniform moment diagram is termed Cm. If M1 = 0.5 M2. Cm. If M1 = 0.5 M2. Cm is equal to:
Solution:
A simple beam having a span of 10m. is subjected to a couple at the left support. At what distance from the left support will maximum deflection occurs?
Solution:
A wooden log is to be used as a foot bridge to span 3m. gap. The log is required to support a concentrated load of 30kN at mid span. If the allowable stress in shear is 0.7MPa, what is the diameter of the log that would be needed. Assume the log is very nearly circular and the bending stresses are adequately met.
Hint: The centroid of a half circular section is 4r/3π and I of a circle is πr4/4.
Solution:
A metals specimen with 36mmθ and has a length L = 360mm. A force of 300kN elongates the length by 1.2mm. What is the elastic modulus?
Solution:
The shear force Sab at a section Z of a cantilever beam of length L with a uniform load W is Sab = W(L – Z) where Z is the distance of the section form the fixed support. The bending moment at the section is:
Solution:
A steel rod having a length of 1m. has a cross sectional area of 100mm2. If it is subjected to an axial tensile force, compute the stiffness of the rod with a modulus of elasticity of 200,000MPa.
Solution:
A cubic meter of soil in its natural state weight 17.75kN., after being dried, it weighs 15.08kN. The specific gravity of the soil is 2.70. Determine the water content of the original soil sample:
Solution:
A structural steel angle 203 x 152.4 has a moment of 10kN-m. The longer leg is parallel to the y-axis and the shorter to the x-axis. The inertial properties of the angle are as follows:
Moment of inertia about the x-axis,
Ix = 33.6 x 106mm4
Moment of inertia about the y-axis,
Iy = 16.1 x 106mm4
Polar moment of inertia,
Ixy = -13.4 x 106mm4
The stress at point A in MPa which is at x-distance of -41.9mm and y-distance + 135.7mm from the centroid.
Solution:
Determine the active pressure per unit length of a vertical cantilever wall 5.5m. high that retains soil with unit weight γ (gamma) = 15.0 kN/m3., soil friction angle φ(phi) = 27(degrees), and cohesion c = 12.0kN/m2. Assume that the wall is very rigid such that no tensile cracks over in the soil.
Solution:
A saturated soil has a unit weigh of 18.85kN/cu.m. and water content of 32.5%. Determine the specific gravity of the soil.
Solution:
A 200mm. by 300mm. wooden section has allowable stress of parallel to the grain of 9MPa. and allowable stresses perpendicular to the grain of 3MPa. Determine the allowable compressive stress in MPa perpendicular to the section inclined at 30 degrees with a line perpendicular to the grain.
Solution:
A reinforced concrete beam has the following properties:
Beam with, b 320mm
Effective depth, d 640mm
Concrete strength, fc’ 25MPa
Reinforcing steel strength, fy 400MPa
Reinforcing steel modulus, Es 200,000MPa
If the beam is to be designed for a balanced condition, find the required area of steel reinforcement in mm2.
Hint: the balanced steel area = 0.75 Asb.
Solution:
The laboratory results of a soil test are as follows:
U.S. Sieve No. Percentage Passing
No. 4 100
No. 10 93.2
No. 40 81.0
No. 200 55.0
Liquid Limit 45.0
Plastic Limit 17.0
The group index in accordance with the ASSHTO Classification system:
Hint: GI = (F – 35) [0.2 + 0.005 (LL – 40)] + 0.01 (F – 15) (P.I. – 10)
Solution:
Two adjacent spans L1 and L2 of a continuous beam with several spans carries a uniform load W1 and W2 on span 1 and span 2 respectively. The two spans are supported at A, B and C. For the two spans under consideration, Ma is the moment at the left or the first span at A, Mb is the moment between the two spans at B, and Mc is the moment at the right of the second span at C. Ra is the reaction under Ma, Rb is the reaction under Mb, and Rc is the reaction under Mc. If L1 = 10m., L2 = 15m., Ma = 20kN-m., and Mc = 25kN-m., and the uniform loads w1 and w2 are both 1 kN/m., the moment Mb is nearest to:
Solution:
A propped cantilever beam (fixed at one end and simply supported at the other end) has a span of 6.0m. The beam carries a uniform load w of 600kN/m. along the 2.0m. length of the span from the fixed end. Compute the moment at the fixed end.
Solution:
A composite beam system is composed of structural steel sections on which a reinforced concrete floor has been attached. The beams have a span of 8.0m. and spacing of 2.4m. The steel section flange width is 180mm and the stab thickness is 120mm. The effective flange width of the composite section according to AISC specification is:
Solution:
The maximum allowable torque in kN-m. for a 50mm diameter steel shaft when the allowable shearing stress is 81.5MPa is:
Solution:
A cantilever beam having a span L of 6.0m carries a concentrated load W of 60kN at mid span. Compute the slope at the free end Assume E = 200,000MPa and Ixx = 60 x 106mm4
Solution:
A simply supported beam with a span of 6.0m carries a vertical load that increases uniformly from zero at the left end to a maximum value of 9kN/m. at the right end. The larger reaction occurs at the right and has a value in kN of:
Solution:
A 200mm. by 400mm. concrete beam is pre-stressed with a final pre-stress force of 500kN at an eccentricity of 100mm. below the neutral axis. Determine the maximum moment that will produce no tension at the bottom fiber.
Solution:
A timber column, 3m. high has a rectangular cross section, 100mm x 200mm and is reinforced over its complete length by two steel plates each 200mm wide and 10mm thick attached to its 200mm wide faces. The column is to carry a load of 1000kN. If the failure stress of timber is 55 N/mm2 and that of steel is 380 N/mm2 and that of steel is 200000N/mm2.
1) Which of the following gives the actual stress of timber using a factor of safety of 3?
2) Which of the following gives the actual stress of steel using a factor of safety of 2?
3) Is the section adequate, not adequate or not allowed by the code?
Solution:
A simple beam has a span of 5.0m. The maximum moment in the beam is 69.0kN/m. The allowable bending stress is 138Mpa. The required section modulus is:
Solution:
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