beam design SS floor deck triangular load 01

Dimensions:

a	b	c
12 in	7 ft	3.1 ft

Problem Statement:
A wooden deck is constructed to support a haystack as shown. The joists of the floor are to be made with dressed air-dry douglas fir lumber with nominal widths of 2 inches. You know that a 14"x18"x36" square bale of this kind of hay weighs 67 lb, and you are assuming the hay in the haystack has the same density as these square bales. (This is probably a conservative estimate, since the bales are probably denser than the stack in reality.) You would like to design the joists to have a factor of safety of 5 against yielding. Determine the following:

(a) The maximum value of the distributed load applied to one joist.
(b) The maximum bending moment experienced by one joist.
(c) The minimum required height h of the joists.
(d) The minimum required section modulus of the joists.
(e) The smallest standard lumber size acceptable to use for joists.

Answers:
(a) $w_{max}$ =
(b) $M_{max}$ =
(c) $h_{min}$ =
(d) $S_{min}$ =
(e) Lumber Choice = 2x4 2x6 2x8 2x10 2x12

be sure to include units with your answers