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Unit IIIA steel beam of I section, 500 mm deep and 190 mm wide has 25mm thick flanges and 15mm thick web. The beam is subjected to a shear force of 400 kN. Calculate the maximum intensity of shear stress in the section assuming the moment of inertia to be 6.45x 10^8 mm4. Also calculate the total shear force carried by the web and sketch the shear stress distribution across the section.


A simply supported beam of span 4 m uses a T section with flange 100 × 10 deep and web 150 × 10 wide. The section is symmetric about vertical axis. The beam carries two point loads 5 kN each placed 1 m from ends point. Find out maximum shear stress in the beam.


A symmetric I section is 150 wide and 200 deep. The flange thickness and web thickness is 10 mm. This section is used for cantilever beam having a span of 3 m and subjected to uniformly distributed load. Find the maximum u.d.l. that can be supported if E = 200 GPa and maximum allowable stress is 180 MPa.


Construct the shear stress distribution diagrams showing salient points :(i) Rectangular section(ii) Symmetrical I-section(iii) Triangular section(iv) Hollow circular section.


Construct the bending stress distribution diagrams showing salient points :(i) Rectangular section(ii) Symmetrical I-section(iii) Triangular section(iv) Hollow circular section.


A simply supported 5 m beam is loaded with point load w at mid. The cross-section of beam is a symmetrical I section 350 mm × 150 mm (overall depth) has a web thickness of 10 mm and flange thickness of 20 mm. The allowable bending stresses in tension and compression are σt = 150 MPa and σc = 100 MPa. Find the safe load ‘w’ on the overhang.


The cross section of a cantilever bracket is ‘I’ where top flange is 120 mm X 20 mm, bottom flange is 40 mm X 20 mm and web is 10 mm thick and 160 mm deep. If in bending the tensile stress is not to exceed 90 MPa and the compressive stress is not to exceed 143 MPa, determine the moment of resistance of the section. If the length of bracket is 1.2 m, find maximum value of vertical point load that can support at its free end.


A Rectangular beam is simply supported at the end and carries a point load at the center. Establish the relation between maximum bending stress and maximum shear stress.


A cast iron beam I section with top flange 80mmx20mm thick, bottom flange of 160mmx40mm thick. The beam is freely supported on a span of 5meters. If tensile stress is not exceed 20N/mm2. Find the safe uniformly distributed load which the beam can carry. Find also the maximum compressive stress.


A steel beam of I section, 500 mm deep and 190 mm wide has 25mm thick flanges and 15 mm thick web. The beam is subjected to a shear force of 400 kN. Calculate the maximum intensity of shear stress in the section assuming the moment of inertia to be 6.45x10^8 mm^4. Also calculate the total shear force carried by the web and sketch the shear stress distribution across the section.


A 250 mm × 150 mm (depth × width) rectangular beam is subjected to maximum bending moment of 750 kNm. The beam is simply supported with UDL all over the length.(i ) Determine the maximum shear stress in the beam(ii) If the value of E for the beam material is 200 GN/m2, find Radius for that portion of the beam where bending is maximum.


Prove that maximum shear for circular section of a beam is 4/3 times average shear.


A cantilever beam of 1.3 m span has a rectangular cross-section 150 mm × 250 mm and carries a uniformly distributed load throughout its length. If the permissible stress in bending is 7 MPa and permissible stress in shear is 1 MPa, find the maximum value of uniformly distributed load, the beam can carry.


A simply supported beam of length 10 m is having UDL load throughout length with intensity 10 kN/m. The cross-section of beam is circular. The allowable bending stresses in tension and compression are σt = 150 MPa and σc = 100 MPa. Find the safe diameter of cross-section.


A simply supported beam carries an udl of 25 kN/m over the entire span. The cross-section of the beam is a diamond shape (i.e. square shape with vertical diagonal and diagonal is 50 mm). If the maximum bending stress is 60 MPa, find the span of the beam. Also find the maximum shear stress developed in the section. Draw the shear stress distribution diagram.


A cast iron pipe with internal diameter 200 mm and external diameter 220 mm is simply supported and its length is 8m. Determine the maximum bending stress in the pipe material when it runs full. The density of cast iron is 70 kN/m^3 and that of water is 9.81 kN/m^3.


A cantilever beam of negligible self-weight carries uniform distributed load 40 kN/m over entire span of 1 m and also has a concentrated load 80 kN at free end, find

a. shear stresses distribution,b. maximum shear stress and its locationc. shear stress at centroidal axis

Section of beam is triangular with base 50 mm and height 80 mm.


A cantilever beam has ‘T’ shaped cross-section. It is acted upon by a clockwise couple ‘M’ at free end. Determine ‘M’ if allowable stresses in bending in tension and compression are 40 MPa and 105 MPa respectively. The flange is 350 mm × 20 mm has a web is 100 mm x 20 mm.


A steel section as shown in the figure below is subjected to shear force of 200 kN. Determine the shear stress at key points and show the shear stress distribution


Determine the width and the depth of the strongest beam in bending which can be cut out of a cylindrical log of wood of diameter d.


A simply supported timber beam of 1.3 m span carries a concentrated load W at the mid-span. The cross section of the beam is 150 mm wide and 250 mm deep. Find the value of W if the permissible working stresses are 7 MPa in bending and 1 MPa in shear.

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