P3 m3 m120 mm50 mm50 mm20 mm20 mm150 mmN/AyThe T-shaped beam shown above is supporting a concentrated load P at its free end. The beamhas an allowable bending stress of allow = 250 MPa and an allowable shear stress of Tallow=100 MPa.a) Determine the distance to the neutral axis (y), second moment of area (I), and the sectionmodulus (S) of the cross-section.b) Draw the shear force diagram (SFD) and bending moment diagram (BMD) of the beam. Onyour diagrams, express the values of shear and moment in terms of the applied load P.c) Determine the maximum value of P such that bending failure will not occur.d) Determine the maximum value of P such that shear failure will not occur.e) Based on your answers to (c) and (d), what is the maximum load P that can be applied to thebeam? Is this beam bending or shear governed?

Maximum bending stress is given by σmax= MmaxI*ymax locate the Neutral axis from bottom we have y =…

P 3 m * 3 m 50 mm 50 mm 20 mm 20 mm 150 mm N/A A The T-shaped beam shown above is supporting a concentrated load P at its free end. The beam has an allowable bending stress of Fallow = 250 MPa and an allowable shear stress of Tallow 100 MPa.

P 3 m * 3 m 50 mm 50 mm 20 mm 20 mm 150 mm N/A A The T-shaped beam shown above is supporting a concentrated load P at its free end. The beam has an allowable bending stress of Fallow = 250 MPa and an allowable shear stress of Tallow 100 MPa.

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Chapter2: Loads On Structures

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Problem 1P

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Concept explainers

Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

P
3 m
3 m
120 mm
50 mm
50 mm
20 mm
20 mm
150 mm
N/A
y
The T-shaped beam shown above is supporting a concentrated load P at its free end. The beam
has an allowable bending stress of allow = 250 MPa and an allowable shear stress of Tallow=
100 MPa.
a) Determine the distance to the neutral axis (y), second moment of area (I), and the section
modulus (S) of the cross-section.
b) Draw the shear force diagram (SFD) and bending moment diagram (BMD) of the beam. On
your diagrams, express the values of shear and moment in terms of the applied load P.
c) Determine the maximum value of P such that bending failure will not occur.
d) Determine the maximum value of P such that shear failure will not occur.
e) Based on your answers to (c) and (d), what is the maximum load P that can be applied to the
beam? Is this beam bending or shear governed?

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Step 2: Moment of Inertia and Section Modulus

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Step 3: (b) Shear force diagram

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Step 4: Bending Moment diagram

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Step 5: Calculation of maximum value of P based on bending for no failure

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Step 6: Calculations of maximum value and maximum load

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