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Problem 2 (50 points): Assuming the beam is made of steel and has a W 6x25...
Use Macaulay's method to determine the maximum displacement in the beam with a uniformed distributed load...
Use Macaulay's method to determine the maximum displacement in the beam with a uniformed distributed load of 10 kN/m applied to the middle section of the beam as shown in the figure below. The beam is made of steel with E = 210 MPa and a cross section in mm as shown. soamm I= axbone where a= 200mm, 6=60omm. 30KN lokN/m 25 kV - Reaction forces Bending moment as a function of a - Integrations BCs -solving for constants of...
A rectangular cross section at a location along a beam in bending is
(a). A rectangular cross section at a location along a beam in bending is acted upon by a bending moment and a shear force. The cross section is \(120 \mathrm{~mm}\) wide, \(300 \mathrm{~mm}\) deep and is orientated such that it is in bending about its major axis of bending. The magnitudes of the bending moment and shear force are \(315 \mathrm{kNm}\) and \(240 \mathrm{kN}\) respectively. Determine the maximum bending and shear stresses on the cross section. Plot the bending and...
A wood beam (1) is reinforced on its lower surface by a steel plate (2) as...
A wood beam (1) is reinforced on its lower surface by a steel
plate (2) as shown in the figure. Dimensions of the cross section
are b 1 = 220 mm , d = 385 mm , b 2 = 190 mm , and t = 25 mm . The
elastic moduli of the wood and steel are E 1 = 12.5 GPa and E 2 =
200 GPa , respectively. The allowable bending stresses of the wood
and steel...
The steel beam has the configuration, loading pattern and cross-sectional area shown in Figure 8. Assuming w = 5 kN/m, d...
The steel beam has the configuration, loading pattern and
cross-sectional area shown in Figure 8.
Assuming w = 5 kN/m, determine:
a) the reactions at each end of the beam
b) the second moment of area of the section about the relevant
axis of bending
c) the maximum shear stress and associated distribution of shear
stresses in the beam
d) the maximum bending stress and distribution of bending
stresses in the beam
0.8 m 0.8 m 0.8 m 8 cm...
Q.2) A boxed beam shown below supports a uniformly distributed load w 180 N/m. Two parts of the b...
Q.2) A boxed beam shown below supports a uniformly distributed load w 180 N/m. Two parts of the beam AB and BC are connected by a pin at B. Using the integration method, find the deflection at B. Assume E = 200 GPa. 40 180 N/m 60 mm 1 m 75 mm Beam Cross-section
Q.2) A boxed beam shown below supports a uniformly distributed load w 180 N/m. Two parts of the beam AB and BC are connected by a...
(a) Determine the maximum compressive and tensile normal stresses in the A-36 structural steel beam shown...
(a) Determine the maximum compressive and tensile normal
stresses in the A-36 structural steel beam shown and define their
locations (location along the beam and on the cross section). (b)
Determine the deflection of point B using the double
integration method. The height of the cross section shown (in the
y-direction) is 5 inches and width (in the
z-direction) is 10 inches, and the average thickness
throughout is 0.5 inches. (Use elastic properties for all
calculations)
ANSWER: (a) max tensile...
2) Below is a rod of length 1 m made of a new steel alloy (E...
2) Below is a rod of length 1 m made of a new steel alloy (E - 200 GPa) which is constrained by tw fixed-fixed supports. The rod has an area of cross sectional area of 100 mm2. There are no residual stresses in the rod. Then, a force of 50 kN is applied to the rod at the location shown. Determine the reactions at the supports A and B. Now, suppose you want to reduce reaction at A and...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w = 10 kN/m throughout and a point load P =10 kN at the midspan of the beam, as shown in Figure Q2 (a). The cross section of this beam is depicted in Figure Q2 (b), which consists of three equal rectangular steel members. Self-weight of the beam is neglected. 30 mm P= 10 KN W = 10 kN/m 200 mm 5 m 5 m...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w = 10 kN/m throughout and a point load P =10 kN at the midspan of the beam, as shown in Figure Q2 (a). The cross section of this beam is depicted in Figure Q2 (b), which consists of three equal rectangular steel members. Self-weight of the beam is neglected. 30 mm P = 10 kN W = 10 kN/m 200 mm 5 m 5...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w = 10 kN/m throughout and a point load P =10 kN at the midspan of the beam, as shown in Figure Q2 (a). The cross section of this beam is depicted in Figure Q2 (b), which consists of three equal rectangular steel members. Self-weight of the beam is neglected. 30 mm P = 10 kN w = 10 kN/m 200 mm 5 m 5...
Use Macaulay's method to determine the maximum displacement in the beam with a uniformed distributed load of 10 kN/m applied to the middle section of the beam as shown in the figure below. The beam is made of steel with E = 210 MPa and a cross section in mm as shown. soamm I= axbone where a= 200mm, 6=60omm. 30KN lokN/m 25 kV - Reaction forces Bending moment as a function of a - Integrations BCs -solving for constants of...
A wood beam (1) is reinforced on its lower surface by a steel
plate (2) as shown in the figure. Dimensions of the cross section
are b 1 = 220 mm , d = 385 mm , b 2 = 190 mm , and t = 25 mm . The
elastic moduli of the wood and steel are E 1 = 12.5 GPa and E 2 =
200 GPa , respectively. The allowable bending stresses of the wood
and steel...
The steel beam has the configuration, loading pattern and
cross-sectional area shown in Figure 8.
Assuming w = 5 kN/m, determine:
a) the reactions at each end of the beam
b) the second moment of area of the section about the relevant
axis of bending
c) the maximum shear stress and associated distribution of shear
stresses in the beam
d) the maximum bending stress and distribution of bending
stresses in the beam
0.8 m 0.8 m 0.8 m 8 cm...
Q.2) A boxed beam shown below supports a uniformly distributed load w 180 N/m. Two parts of the beam AB and BC are connected by a pin at B. Using the integration method, find the deflection at B. Assume E = 200 GPa. 40 180 N/m 60 mm 1 m 75 mm Beam Cross-section
Q.2) A boxed beam shown below supports a uniformly distributed load w 180 N/m. Two parts of the beam AB and BC are connected by a...
(a) Determine the maximum compressive and tensile normal
stresses in the A-36 structural steel beam shown and define their
locations (location along the beam and on the cross section). (b)
Determine the deflection of point B using the double
integration method. The height of the cross section shown (in the
y-direction) is 5 inches and width (in the
z-direction) is 10 inches, and the average thickness
throughout is 0.5 inches. (Use elastic properties for all
calculations)
ANSWER: (a) max tensile...
2) Below is a rod of length 1 m made of a new steel alloy (E - 200 GPa) which is constrained by tw fixed-fixed supports. The rod has an area of cross sectional area of 100 mm2. There are no residual stresses in the rod. Then, a force of 50 kN is applied to the rod at the location shown. Determine the reactions at the supports A and B. Now, suppose you want to reduce reaction at A and...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w = 10 kN/m throughout and a point load P =10 kN at the midspan of the beam, as shown in Figure Q2 (a). The cross section of this beam is depicted in Figure Q2 (b), which consists of three equal rectangular steel members. Self-weight of the beam is neglected. 30 mm P= 10 KN W = 10 kN/m 200 mm 5 m 5 m...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w = 10 kN/m throughout and a point load P =10 kN at the midspan of the beam, as shown in Figure Q2 (a). The cross section of this beam is depicted in Figure Q2 (b), which consists of three equal rectangular steel members. Self-weight of the beam is neglected. 30 mm P = 10 kN W = 10 kN/m 200 mm 5 m 5...
Q2 The 10 m long simply supported beam is subjected to a uniformly distributed load w = 10 kN/m throughout and a point load P =10 kN at the midspan of the beam, as shown in Figure Q2 (a). The cross section of this beam is depicted in Figure Q2 (b), which consists of three equal rectangular steel members. Self-weight of the beam is neglected. 30 mm P = 10 kN w = 10 kN/m 200 mm 5 m 5...
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