civil engineering

1) Which of the following gives the balanced steel ratio.

2) Which of the following gives the depth of the compression block.

3) Which of the following gives the nominal moment capacity of the beam.

Solution:

Section 5.9.5.2.1 of the National Structural Code of the Philippines specifies the minimum thickness as shown on the table apply for one way construction not supporting or attached to partitions or other construction likely to be damaged by large deflections, unless computation of deflection indicates a lesser thickness can be used without adverse effects.

Minimum thickness of Non-Prestressed Beams or One Way Slabs Unless Deflection Are Computed.

		Minimum thickness, h
	Simply Supported	One end condition	Both continuous	Cantilever
Member	Members not  supporting or attached to partitions or other construction likely to be damaged by large deflections.
Solid one-way slab	L/20	L/24	L/28	L/10
Beams or ribbed one-way slabs	L/16	L/18.5	L/21	L/8

For the continuous beam shown

1) Which of the following gives the minimum thickness of beam B-1.

2) Which of the following gives the minimum thickness of beam B-2.

3) Which of the following gives the minimum thickness of beam B-3.

Solution:

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A cantilever prismatic beam is 8m. long and propped at one end. EI = 1750 N.m²

1) Which of the following gives the moment induced by a unit rotation at the propped end.

2) Which of the following gives the moment induced at the fixed end.

3) Which of the following gives the reaction at the propped support.

Solution:

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A rod is connected to a pin at A and a chord at B as shown. It holds a cylindrical drum which weighs 176N. The drum has a diameter of 1m.

1) Which of the following gives the force between the drum and the rod.

2) Which of the following gives the force in the chord BC.

3) Which of the following gives the reaction at the pin at A.

Solution:

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1) Which of the following gives the acceleration of the car

2) Which of the following gives the normal force on the front wheels.

3) Which of the following gives the minimum coefficient of friction needed so that motion is possible.

Solution:1) Tensio:

F_b = 0.60Fy

2) Compression:

For member meeting the requirements of Sect. 4.9.1.2, having an axi of symmetry in, and loaded in, the plane of their web, and compression on extreme fibers of channels bent about their major axis:

The larger value computed by Formula (4.5-6a) or (4.5-6b) and (4.5-7), as applicable (unless a higher value can be justified on the basis of a more precise analysis), but not more than 0.60Fy.

Or, when the compression flange is solid and approximately rectangular in cross-section and its area is not less than that of the tension flange:

In the foregoing:

I = distance between cross sections braced against twist or lateral displacement of the compression flange, mm. For cantilevers braced against twist only at the support, I may conservatively be taken as the actual length.

r_t =  radius of gyration of a section comprising the compression flange plus 1/3  of the compression web area, taken about an axis in the plane of the web, mm.

A_f = area of the compression flange, mm³

C_b = 1.75 + 1.05(M_1/M₂) + 0.30(M_1/M₂)² but more than 2.3, where M₁ is the smaller and M₂ the larger bending moment at the ends of the unbraced length, taken about the strong axis of the members, and where M_1/M₂ the ratio of end moments, is positive when M₁ and M₂ have the same sign (reverse curvature bending) and negative when they are of opposite sighs (single curvature bending). When the bending moment at point within an unbraced length is larger than that at both ends of this length, the value of C_b may be computed by the formula given above for frames subject to joint translation, and it shall be taken as unity for frames braced against joint translation. C_b may conservatively be taken as unity for cantilever beams.

A simply supported beam having a span of 8m. is laterally unsupported is made up of A36 steel with Fy = 248 MPa with the following properties:

b_f = 0.210m                             r_t = 0.073m.

S_x = 0.002077m³*********t_f = 0.016m.

d = 0.533m.

1) Which of the following gives the slenderness ratio above which the beam would be considered long.

2) Which of the following gives the allowable bending stress.

3) Which of the following gives the maximum uniform load that can be carried by the beam.

Solution:

1) Which of the following gives the reaction at the fixed end.

2) Which of the following gives the maximum torsional stress.

3) Which of the following gives the angle of twist of the shaft.

Solution: